So, in theory, we're running. Here we go. Tutorials. Math 12. New page. Folks, as you come in, grab one of those, please. Transformations. Tutorial. The basic, if I was going to summarize the entire unit in two words, well, three words, everything is backwards is what I would summarize the entire unit with. In other words, if you're not sure what to do, do the opposite of what the equation seems to suggest. So, we defined function notation. We said we're going to write all of our equations as y equals a bracket f minus, or f of x minus b. Oh, hang on, Mr. DeWitt, get this right. A little rusty clearly. b bracket x minus c close bracket close bracket plus d. We said every single function. Pardon me? No, don't write on them, please. Sorry, good question. I need to reuse those, and we don't have extras. So, don't write in the little test booklets, but we're going to use them for some sample questions later on. We wrote most of our equations in this function notation. Now, remember, for what it's worth, you could actually take the time to rewrite this, grab one of those, as a bracket y minus d close bracket equals, and technically we won over a f of b bracket x minus c. Now, if you took the time to rewrite everything like this, where you got all the y stuff next to the y, and all the x stuff next to the x, then my everything is backwards rule held. Then it was just fine. So, we looked at stuff like this. If you want to get out that little booklet that I gave you, and if you'd be so kind as to open to the first test, I think it's like page four. This question here is the one you're looking for. Now remember, your provincial and your mock provincials are going to have a non-calculator section, and it's going to be 16 questions. A lot of it will be transformations, because that lends itself to non-calculator questions. So, it says the graph of y equals f of x is translated one unit to the left. Let's copy that into here, Mr. Dewick, so that you can print the question. Which equation represents this translation? Now, probably most of you are going, yeah, I can do this already, as is no problem. But here's what we said. We thought in terms of replacements. We said, first of all, if you're translating to the left, is that horizontal or vertical? Left, is that a horizontal or a vertical? Horizontal. Horizontal. That means you're replacing x with something. And what are you replacing? Well, if you want to move one left, what you're really doing, Matt, is you're replacing x with x plus one. Everything is backwards. One left in the negative direction meant replacing x with x plus one. So if my original equation was y equals f of x, that would become y equals f of replace every x with an x plus one, and now the answer is clearly c. Everything is backwards. Right? Let's look at number two. Which of the following represents the transformation of y equals g of x if it's horizontally expanded by a factor of three over two and then horizontally translated c units? I'm just going to work through some of these questions kind of as a refresh our memory gig, and then we'll take specifics and every so often go off on a tangent. See what is now, Matt? Good. Horizontally expanded by a factor of three over two, that means you're going to replace x with what? Defining silence. Everything's backwards. Two over three x. Then you're going to horizontally translate at c units. That means you're going to replace x with x minus c if you want to move at c units to the right. So if I walk through the transformations, I would have this y equals g of, first of all, I would replace the x with a two over three x, and then I would replace this x with that right there. Everyone grab the little test there, please. The test thingy booklet. So when I do that, I'll get y equals g of two thirds, and I guess I'll have to put it in brackets. x minus c. What's the correct answer here? Don't all shout it out at once. D. One of my friends who typed up a review, he summarized everything this way, and I'll put this one online under transformations review as well, eventually. He said, here's what you want to remember. Anything here is a vertical stretch, and it's not backwards because it's already been moved over. If it was on this side, it would be backwards. So a one-half over here is a vertical expansion by a factor of two, because a one-half becomes a two on this side anyhow. Anything next to the x is horizontal. This would be a horizontal expansion of compression. If the absolute value of b is bigger than zero, in other words, if b is a fraction, sorry, if b is a bigger than zero, that should say bigger than one, I think, and bigger than one, then it's going to be a compression to fix that typo a bit later.  You could also reflect about the line y equals x by replacing the x and y with each other. We called that taking the inverse, and we had all our translations. Then we had to remember the order. The order that we did everything was, we said factor first, then expansions, compressions, then reflections, then slides. Let's look at a few more. Hello, this thing. So, number three. Now, there's only so many questions we can ask you that say, find the point or tell me the transformation. Eventually, we'll try and mix and match a little bit. We'll start asking questions about things like the domain and stuff like that. So, looking at number three, turn that off, I remember the screencast. Graph of y equals f of x is given below. The function is transformed to that. What's its domain? Now, when I look at this, y equals f of 2x minus 6, the alarm bell goes off right now because it's not factored. Anytime they give me one that looks like this that's not factored, the first thing I have to do is factor it. I'm going to rewrite this as y equals f of 2 bracket x minus 3 because Jeff, this has not been moved 6 to the right. How far has it really been moved? 3 to the right. Now, let's see if we can't answer the question. Now, this is already a bit of a more difficult one because they haven't even given me a specific point. They've given me a point p, q. Now, if you don't like that, feel free to temporarily make up nice numbers. I could say I'm going to pretend it's 4,8 and I'll see what happens to the 4 and the 8 and see if I can translate that there. But we're going to try and do this one algebraically. So, right now, what's the domain of this function before I do anything to it? Well, the domain is everything left and right. How far to the right does this function go? Forever. How far left does this function go? So, right now, the domain is everything to the right and touching p. Now, domain, is that horizontal or is that vertical? Horizontal, because as a trick question, they could have given me a bunch of vertical stuff and the answer would have been, you know what, no change if it's domain. The vertical stuff doesn't affect the domain anyways. So, they could have put a plus 1 here or a negative 1 half here. Who cares? That's not going to affect the horizontal. This is definitely horizontal. What's that do? Horizontal or vertical? Horizontal. Expansion or compression? Is that two times as big or half as big? Half as big. Why? If you're not sure, everything's backwards and it is next to the X. So, first of all, my domain would become that. I'm not done yet. What's that mean? I'll give you a hint. Three. Three right. I would take this number and I would add three to it. Do I see that sitting there anywhere? Yeah. Is that okay? Next one. Don't want that. Want that guy. Number five, how does that graph compare with that graph? Yeah, you're going to need to turn the page. Those of you who score are keeping it home. What I'm going to do is I'm going to go through the test. That's going to jog most of the cobwebs off your brain and then I'll do specific weird ones. I'll give you a couple of provincial exams to look at as well. And I'll give you a few hints about the mock and things that, you know, preview of coming attraction type deals. Well, is this in okay form? Am I okay with this? Is there anything I need to factor? I'm okay with this. Normally, on our graphing calculators, we move that one quarter over to this side and it became a four. But it's here. If it's next to the Y, everything's going to be backwards. So, I'm going to look at this one quarter. It's vertical or horizontal and how do I know? Vertical? Why? Because next to the Y, that often gets rid of half-year-long answers. It didn't in this case. Expansion by four or compression by one quarter? And look, can you grab one of those practice tests there, please? Sorry? Expansion by four. So, already I would cross out B and I would cross out D. X plus two means what? Two left. The answer, expand by four. Two left. The answer would be A. Number six. Can I get this all in one page? I can if I shrink it. Fifth page. Make it a little larger, Mr. Dewick. Not too big. Try that. Click. This is a good one. Come on. Okay. Says this graph has transformed four different ways to two graphs, one, two, three, and four. Okay. What's this one look like? Sorry? Inverse? Now, let's convince myself this point right here looks like it's around, let's say, negative three, comma, negative one-ish. Does this point here look like it's around negative one, comma, negative three-ish? Oh, did the X and Ys switch around? I think it's inverse. So what's the symbol for inverse? Little negative one, not one over f of X. Y equals, if I'm picking answers, I'm going, haha, no, no. What do you think they did with those two graphs? Looks like the simplest would be a vertical reflection. So I think this is Y equals negative f of X. Put a negative outside the brackets, vertical. Now, technically, I'm done because I just eliminated C. And if you're a good multiple-choice test writer, I would say stop. But since we're doing review, let's keep going. How do I know that this here is a reciprocal? And where do the asymptotes occur? Wherever my original graph has what? Zeros. Wherever my graph is zero high, my reciprocal will have asymptotes. Which points won't change? What was the fancy word for points that didn't change? Do you remember? Yep. Invariant. Which points would be invariant anywhere, how high or how high? One or negative one high. So if you're doing your reciprocal graph, what I always do is I put big, thick dots anywhere one high or negative one high. Then I draw in the asymptotes. And then I think bigger becomes smaller, smaller becomes bigger, because they're reciprocals of each other. So this would be Y equals one over f of X. And I think it looks like this one is a horizontal reflection. Y equals f of negative X. We're good. Let's keep going. Let's make it back to page width. We did number six, right? Let's look at number seven. And again, I got to shrink this down a little bit. One more, but I think that'll fit. Okay. The graph of that thing is shown below. Which of the following is the graph of Y equals absolute value of f of X minus two? Well, there's two things going on here. Absolute value. And what would a minus two outside the brackets do? I heard both answers. It's two down or two right. Which one? I heard them both again. Someone convinced me that they're right or someone else is wrong. If it was two to the right, where would that X, sorry, where would that two have to be? Inside right next to the X. Is it inside right next to the X? Okay, so I think it's two down. Now one question students have is, what's the correct order? Do I do absolute value first and down first? This one I think I would go down first and then absolute value. I think if it said this, that's how I would write do the absolute value first and then go down. Which you're going to treat the absolute value sort of like brackets in our bed mass order of operations scale. So two down would look kind of like this. And then what would the absolute value transformation do? Flip what up? Anything below the X axis, that section, will flip above the X axis. I can get a specific point there. Yeah, it would look something, boy, my graph is bad. Let's try this arm a little better. Mr. Duk. It would look something like that. And I'd do it with graph paper a little bit better. Am I totally off, Mr. Kamosi? No, this one should go through three if it's symmetrical. But let's just pretend I can't draw.  The graph paper that this thing has built in has been a godsend. Anyways, which one of these looks right? I think C. Sesame Street is brought to you today by the letter W. Turns out the letter W is an absolute value graph that was moved down first. Who knew? I thought the letter W was just two Vs next to it. It always bothered me, Mr. Duk. Why do they call it W and not WV? It's a series of life that we just have to live with. I know. Am I the only one that bugged when I was growing up? Yeah, but a V is still a V. I don't think girls do a V like that. And if they do, I'll never understand. Okay. The partial graphs of two functions are given below. Hey, I can clip this one. It'll fit. Which equation for Y equals G of X, that's this one here, represents the transformation of that? Well, I do notice they gave me a key point. Zero comma negative two became zero comma negative a half. What have they done? I heard someone say inverse. And I heard someone say reciprocal. Please tell me which is it. Inverse or reciprocal? What does inverse mean? When you see...  That's inverse. That's reciprocal. How do you find an inverse? Switch the X and Y around. In other words, this would become two comma... Sorry, negative two comma zero. Did it become negative two comma zero? What does reciprocal mean? Take your heights and make them one over. The height. Your X's don't change because we're saying if f of X is actually the same as Y, this is saying graph one over Y. It's your heights that change. Your X's stayed where they were. In other words, if your original graph had a point there, your new graph had a point there, the only exception was zeros became asymptotes and your graph was undefined there. But everywhere else, your X's just became new points, but they didn't change. Anyways, I'm pretty sure this is a reciprocal, not an inverse. Inverse would go through negative two comma zero. The inverse would look something like that. And you could always check for the inverse because there are always reflections about the line Y equals X, except of course I have my inverse pointing the wrong way, Mr. Kamosy. The inverse would look something like that. For those of you who are scorekeeping at home, multiple choice, select the best answer, an approved calculator may be required. I'm going to try and do this without a calculator. Oh, here's another range question. Domain and range in many ways, although they look nastier in the transformation section, they're actually easier because if they ask me about the range, Jeff, I'm already ignoring all the horizontal garbage. I don't even care. Because you know what? That plus four can't change the range, Megan. It can't. So who cares? And if they had a two in there, who cares? I've eliminated a lot of my thinking. It's actually harder to find the point than it is to find the domain and the range. All I have to do is write down what's the range of the original function. So here's my original function. What's its range before I do anything? Why? Less than or equal to one. Now I just walk through all the vertical stuff that's going on here. Horizontal or vertical? Horizontal, that's not going to change the range. What's that going to do? One down. Oh, no, wait a minute. That's not one down. One of the most common mistakes. I don't remember when we went over the transformations test. Most you were kicking yourselves for sloppy math. There it is. While we're looking at this question that they gave us, what if they had done this? Now what's the range? Piece of cake. Easy.  My original range was why is less than or equal to one. Is this factored already? Well, in the middle there it's not, but that's all domain garbage. So I'm not going to waste my time. This and this are nice factored separate. I'm happy with this. So correct order. Expansions, compressions. What's that going to do? I'll give you a hint. It's either expand or compress. Math. Expand because over here it would be a one half and everything's backwards. When you move it to this side it's a two, no longer backwards. What's that factor of? So that's going to become a two. Expansions, reflections. Check. Sorry, expansions, compressions. Check. The next thing we do is reflections. What's that going to do? Vertical reflection. How's it going to affect my range? Negative. What's that? Pour down. There you go. They could even be really snarky and give me the range algebraically. In other words, they could have said something like this. I'll do a domain question instead. Sure. While picking up where we left off, Mr. Dewick made a mistake. That's the correct answer right there. If you're not sure why that's the correct answer right there, see Mr. Dewick or ask Mr. Kamosy because he's better at math than me. There. Save that one. No one's going to notice online. That's the difficulty with doing this for posterity. Number 10. Which transformation to y equals g of x might change both the domain and the range? Okay. Well, what will that do? Vertical or horizontal? Vertical. Can that possibly change the domain then? No. How about that? That's a vertical. No. How about that? That's a horizontal. Nope. What's this a symbol for? That's not an inverse. What's the x and y? Does that mean you would just switch the domain and range around too? If they weren't equal to begin with, they would definitely change. They would become each other. That was actually a nice little shortcut we often use. I use that quite often if I had to find the domain of a log graph. I'm not great at log graphs. Exponentials I'm good at. I would find the range of the exponential. That was the domain of the log graph and the range. On one of your mocks, you are going to have a before and after graph. Something like this. However, when I look at this question, first thing I would do, the alarm bell would go off with my students. My students don't even twitch anymore. I got you there. Okay. This one here? Not factored. These ones are all okay, but if I got a coefficient inside the brackets and a slide inside the brackets, I need to rewrite this one. This is actually f of, I'm going to factor out the negative 2. When I do that, I recognize ooh, this is one right, not two left. Now let's see what's going on here. First of all, how wide is this graph in total? One, two, three, four, five squares. How wide is my new graph in total? One, two, three, four, five squares. Do you think we've done a horizontal stretch or expansion at all? Compression or expansion? No, you know what? I don't think that can be right because that's got a horizontal expansion compression. I don't think that can be right because that's got a horizontal expansion compression and that would change how wide this graph was. No, no. I noticed that the long side and the V is at the bottom. Here the long side and the V is at the top. I think there's a vertical reflection that's occurred. It doesn't help me at all. You know what, there's been a vertical reflection there too. In fact, there's also been a vertical expansion and both are remaining answers. What I need to do is figure out have I gone two left or two up? Well, this point right here, how high is it originally? Zero high. If I did a two left, how high would it end up? Zero high. I think it corresponds to that one. Is that one zero high? I think this one has been moved two up. I think it's this one here. I usually do use a process of elimination for certain key points. I'll look at V shapes right now. It's three high. Negative three high right there becomes positive eight high. I think they doubled it and reflected it. Sorry, I think they reflected, doubled and moved it two up. Double it, becomes negative six, reflected becomes positive six, move it two up, becomes positive eight. We're blazing. It says the given quadratic function has a positive X intercept. Check. A negative X intercept. Check. And a negative Y intercept. Check. Which of the following statements are true? The inverse will have a positive Y intercept, a negative Y intercept, and a negative X intercept. The graph of the reciprocal will have no X intercepts and the positive Y intercept. Hmm, I don't know. But they seem to think I can figure it out, so let's see. Let's answer the inverse part first. A symbol for inverse. How do I find an inverse? Why? So I guess that means that these two will become Y intercepts instead of X intercepts, and this will become an X intercept instead of a Y intercept. So read that carefully. Is statement one true or false? If I switch the X and Ys around, that's what my original would become, would it not? I think true. Statement one. I'm happy with that. Statement two. Sketch the reciprocal. Now what will the reciprocal look like? It will be an asymptote right there. An asymptote right there. Let's say one high is right about there. Let's say one high, negative one high, negative one high, I'm just eyeballing it, making up numbers. One high is right about there. Have an example clip, please, right there, Jessica. This would look like this. Bigger becomes smaller. Smaller becomes bigger. Gets closer and closer to the X axis. What about here? It gets further and further from the X axis, gets further and further from the X axis, and it would kind of do something like this. The Y intercept would become a reciprocal. I'm probably a little bit off. If this is 1.5, it should be the reciprocal of 1.5, but it would look something like that. Does that match this description? This graph will have no X intercepts. That is true. And the positive Y intercept. Coming back to you folks, Coleman's nodding, others aren't. I like number 13. I like number 13. Number 13 is a nice question, except it's a different variation that I also like. Some of you haven't had me before. Helen, why would I say that I like a question? Helen, why would I say that I like a question? You didn't hear me say that. Are you just really a good student and you pay attention to these things when you're studying? Let's look at number 13. Now, here instead of finding an inverse graph, it wants me to find an inverse equation. Well, how do I find an inverse? Switch the X and Y. This is one of the few times to me function notation is more confusing because there's an X sitting in there. I don't like that. I replace the F of X with a Y just so I have a little bit less to keep track of. And now I'll do the inverse. How? Switch the X and Y around. Absolutely. Equals negative 2 bracket Y plus 6 all squared plus 3. And now I stop and I say, oh, jeez. I guess they went and they got the Y by itself. Sometimes they don't. Sometimes they're okay with that. I've seen that as the correct choice before. They want me to get the Y by itself. How would I get the Y by itself? That's what I said. Thank you. Sorry. How would I get the Y by itself? From both sides, I would go X minus 3 equals negative 2 bracket Y minus 6 all squared divide by negative 2 and I'll get X minus 3 over negative 2. Now, by the way, I'm noticing there are no negative 2s here. We may have to work a little magic in just a second. Yeah, I agree. I'm going to square root and then plus 6. I think what they did with this negative is they divided the negative into the top and the bottom. I think they rewrote this as 3 minus X over 2 equals Y minus 6 all squared. How did I pick up on that? I didn't see any negatives kicking around down here and I saw a couple of 3 minus Xs. In fact, I'm kind of already thinking no and no. Now what? Square root isn't quite right. It looks like it's going to be plus or minus square root. When you square root both sides of a polynomial, plus or minus. So I'll have Y minus 6 equals plus or minus the square root of 3 minus X over 2. And last step, how would I get the Y by itself? Plus 6 inside the square root or outside the square root? Outside. That ends right there. Looks like the answer is A. But here's the question that I really have some strong affection for. Given Y equals 2X all over 5X plus 3 do I want an X on the top and on the bottom or is that going to get yucky? Nah, that'll work. Find the inverse. How do I find an inverse? Switch the X and Y around. If this shows up, it'll probably be a written question. And I would probably give you a mark for doing that. Now what? This seems to be where students freeze and it drives me crazy. Ready to snap? Well, little Miss Mander who has me in physics, yes? Cross-multiply. That is one fraction equals one fraction. This is really X bracket 5Y plus 3 equals 2Y. And now I'm going to get rid of the brackets. I'll get 5XY plus 3X equals 2Y. Now what? I want to get the Y by itself. We're going to move this over to this side. Get all my Ys to one side. So I'm going to go 3X equals 2Y minus 5XY. Now this is yucky because how many Ys do I have here? Two. How many would I prefer to have? How? Facture it. Absolutely. This is going to become 3X equals Y bracket 2 minus 5X. And now I can get that Y by itself really easy. Divide. I'll get Y equals 3X all over 2 minus 5X. That one has popped up on a provincial every so often as well. This is a 5 mark written question. To me, that's getting 5 marks for really doing math 10. Cross-multiplying in factory. The only math 12 is how do you find an inverse? Although actually you did it in math 11. So whether it shows up again, I don't know. They might have complained about that being too easy a question for 5 marks, but there you go. Facture a little handy-dandy test. Let's see. An invariant point is a point that remains unchanged using the graph of Y equals G of X to determine the number of asymptotes and the number of invariant points for the, well, for that thing. How about just to practice maybe we graph this? Again, by the way, don't write on these test booklets. Right? Is that a note? Okay. You're passing no notes to each other? Love notes to each other. I did play a romantic math song before we came in. I know. It's what happens when you're late. Yeah, I did. You were here at about 4 after 3. You ready? If they gave me this and they just said, hey, graph that. Let's do it. First thing I would do is invariant points are going to be anywhere 1 high or negative 1 high. That's invariant. That's invariant. And that's invariant. By the way, how many invariant points are there for this multiple choice question? 5. Wrong, wrong. Then it's going to have asymptotes. It's going to have asymptotes wherever the original graph has a root has an X intercept. It touches the X axis. It's going to be a vertical asymptote right there. Vertical asymptote right there. And a vertical asymptote right about there. If I eyeball it. How many asymptotes are there going to be? 3. Matter of fact, the correct answer is that guy. But let's graph this.  This guy here. As I walk this way, my original graph gets closer to the X axis. What's the reciprocal of getting closer to the X axis? It's going to shoot off to infinity. Well, negative infinity, fine. As I walk, go back to my invariant point, as I walk this way I get closer and closer to a height of what? Negative 2. What's the reciprocal of negative 2? Negative a half. I'm going to get closer and closer to a height of about negative a half. I'll just slide ball it, but I'm pretty close. Oh, and it looks like if I stand on this invariant point as I move to my left, I also get closer and closer to a, well, a reciprocal to a height of negative 2, reciprocal negative a half. What about as I move to the right? Well, my original graph gets closer and closer to the X axis must shoot off to infinity. What about this middle chunk right here? Well, there's a point right there. As I move to the left, gets closer to the X axis, shoots off to positive infinity, shoots off to positive infinity. The highest this gets is 2. The reciprocal of 2 is a half. I think right there would be one half high. And over on this point, as I move to the right, there's no graph, so I'm not going to put anything there. As I move to the left, it's getting closer to the X axis, and it must shoot off to infinity. It would look something like that. We're okay? Nothing? I'm going to put my microphone out on my little software program here. Graph of Y equals H of X is shown below. Which graph represents X equals H of Y? What have they done here? When they say X equals H of Y? Switch the X and Y. What's another fancy word for that? Inverse. So really, all I'm looking for is a graph that seems to be a reflection about the line Y equals X. You know what? This is 0, 4. Those two will just flip over each other. So I'm looking for a graph that still goes through 4, 0 and 0, 4. What about this endpoint right here? What's its coordinates? 6, 6, 6. What's the inverse of 6, 6? So I'm looking for a graph that still goes through 4, 0, because that would become 4, 0. And still goes through 0, 4. Because this would become 0, 4. And goes through 6, 6. I think there's only one graph that fits that, isn't it? I didn't print that one in my tutorial, sorry. Turn the page. Because when you switch 6 with a 6, but you still get a 6, 6. Does the graph not go through 6, 6? I think it does. 6 over 6 up. What's the inverse of 6, 6? 6 because you switch the X and Y around. The graph itself will be on the line Y equals X, and it's automatically its own inverse. So 5, 5, 4, 4, 4, 3, 3, 2, 2, 1, 1, 1, 0, 0, negative 1, negative 1. Those are all inverses of each other. Mr. Kamosy, have I made any mistakes lately or not? Still not right? Okay. I'm going to throw this online. So we're just going to scroll back. This one here. I need to draw it out. We're not going to throw one like that. Here we go. These are the following questions. So I will definitely on your mock give you some points to do some math with. I find for me the easiest thing to do is list the transformations in the proper order. And then I usually just write the point down, work my way outwards, left and right. So I glance. I'll show you what I mean. I glance at this. Do I need to factor this or is this okay? It's okay. Let's list what's going on. What's that one half? Vertical or horizontal? Vertical by two or by a half? What's that? What type of reflection? Now remember, the phrase they'll use is a vertical of reflection about the x-axis. I always just think vertical reflection because as soon as I mention x, I start thinking horizontal right away. But in the terminology, they'll say it's a vertical reflection about the x-axis. And yeah, it's true. That's what you're flipping around. I just choose to say vertical reflection. Vert reflection. What's that? Four. It's next to the x, so it's got to be a horizontal. It's right next to the x backwards. Yeah, four right. Then what I do is I write down the x-coordinate and the y-coordinate. And I'm just going to work my way outwards. Vertical by a half? That's going to become a three. Vertical reflection? That's going to become a negative three. Four right? That's going to become a negative eight. I find that works for me just kind of working outwards. Let's do a couple of yuckier ones. Let's see what they got here. Let's do a ball. Okay. This one here needs to be factored at all. Nope. Okay, let's list the transformations then. Expansions, compressions, nothing vertical. Oh, horizontal. Compression. By one third. Because it's next to the x and everything backwards. Reflections, no. Oh, horizontal reflection. Then what's that minus eight mean? Eight down. And then I'll write my original point again, which was negative 12, six. And once again, I'll just work my way outwards. Horizontal compression by one third. That's going to become negative four. Horizontal reflection, that's going to become positive four. Eight down, that's going to become negative two. I see a reciprocal and I see a plus six. A six up. Do I do reciprocal first and then go six up? Or do I go six up first and then do reciprocal? If they wanted me to go six up first and then do reciprocal, I think they would have done one over g of x plus six. I think that's the head. Do that first and then take the reciprocal of your answer. I don't recall ever seeing one that yucky. And even reciprocals with a twist, don't happen all that often. They've only started showing up a little bit lately the last couple years. There will be a reciprocal with a twist on your mock though. What do I mean by with a twist? It won't just be a straight reciprocal. It'll be a reciprocal with a reflection maybe or with a stretch. But I'm not going to give you a reciprocal with a vertical stretch, a horizontal stretch, a horizontal reflection on a slide. I'm not going to hammer you. So we have reciprocal and six up. Negative 12,6. Reciprocal. Sam, this is what I meant earlier when I said your x's don't change, only your height changes. But your x stays the same. Six up! Add six to it. Reciprocal of six is one sixth. And then six up. I guess the answer. We pause. Is that okay? Sure. I know sometimes a little hamster on the wheel. Just give me a little kick. There we go. What about this one? Well, what's that to? Vertical or horizontal? Vertical what? Expansion. And absolute value. Now, look carefully. Do they want me to do absolute value first and then expansion or do they want me to do vertical expansion and then absolute value? Which one do they want me to do first? And I'll compare it with this. One of these things is not like the other. One of these things just doesn't belong. No, that's sorry. One of these things has expand first, then absolute value. One of these has absolute value and expand first. Think about the bed mass rules. Here I think absolute value first, then double your heights. Here, double your heights first, then absolute value. So here we have absolute value and then vertical expansion. We're starting out at negative 12 comma 6 when I take the absolute value of the height. What's the absolute value of 6? 6, vertical expansion by 2 is going to become a 12. Nearly there. I think. Determine the image of point A. So now they're going to give me a different order, perhaps. Every once in a while they'll walk you through the wrong order just to see if you can follow the instructions, make the substitutions, and come up with the equation that they want. Hey, no laughing. We're learning. I find math hysterical, Mr. Doock. Okay, fine. So, determine the image of point A. What was point A? It was negative, I forgot. Negative 12 comma 6. So there's negative 12 comma 6, and now we're going to go in the following order. Reflect about the line y equals x. What? Oh, yeah, that was another way of saying inverse. So it's going to become 6 comma negative 12, which you have to lie around. Horizontally expand by a factor of 2. One left. Let's make that an 11 and not a smear. Now there is a written section. I'm actually not going to walk through a whole bunch of these. Instead, I'm going to say, are there any specific weird ones that you are wondering about, either from your provincial exam review or your homework. Remember, you guys all have four exams, right? And if you don't, they're online. I think if not, they will be shortly at thepitmath.com. Click here for Mr. Doock stuff. Principles of Math 12. I'll set up a provincial exam, or an exam review folder or a year end review folder. Something like that. I'll put stuff in there by unit, and I'll put blank exams in there as well. I just wanted to show you a couple of exams. So here is the August 08 I think, or sorry, August 04 exam. And just letting you know kind of some of the stuff that you're going to see. That's trig, trig, trig, trig, trig, oh that's log. This was conics. We don't do that anymore. But here's one number 25. This equation represents the graph of y equals g of x after it's reflected in the line y equals x. C? What's C? Reciprocal. Is that the same as inverse? No. So we have three ways, well two ways we can write inverse. The negative one, or x equals f of y. Switch the x and y around. How is that graph related to that graph? Vertical or horizontal? Vertical. So right away you're getting crossing off b and d. Now it's a true or false question. You've got a 50-50 chance of guessing, right? By a half or by two? By a half. Here's a bit of a range twist. So if my original range is from negative one to positive two, what's my new range? When I take the, is that inverse or is that reciprocal? Okay. Here, I would probably just make a sketch. What's my original range? Well, my original range it says is from negative one to positive two. The simplest possible graph would be something, I'll just pretend it looks something like that originally. If I take the reciprocal, oh, invariant points, negative one high, one high. Vertical asymptote. What will this line do? Shoot off to infinity. Technically negative, so technically small, but I just say it shoots off to negative infinity. Here, as I move to the left, it's getting closer to zero. Get further away from the x-axis. Here, well, it's going to get closer to the x-axis. What's the highest this line goes? The lowest we go is to one half high. Okay. There's my range. There's my picture. Now what's the range? Everything below negative one, so that's wrong and that's wrong. Because that's missing y is less than or equal to negative one. How would I write this? Everything above or touching. There you go. That was number 27 on this exam. I'm willing to bet that the next question is not a transformations and I lose that bet. Okay. I thought this was the nasty one that year. Hit page. Hit width, Mr. Duke. Yep. That's fine. Not a detention. Just put the test back there, please, when you're done. The function y equals f of x is graphed to the left below. Determine an equation of the function shown on the right. Okay. Key points. Well, first thing I would say is how wide is my original function? 24. How wide is my new function? 12. We've definitely had a horizontal compression by that's a waste of my time. Shoot. They all have a horizontal compression. Nothing vertical looks like it's occurred. It went from 0 to 8 high. It's still 0 to 8 high. Now, looking at these, the alarm bell would go because these three aren't factored. Got you one last time. One for the road, so to speak. You feel good with that adrenaline rush now, though, don't you? Oh, yeah.  Now, this graph here says it's been moved 3 in which direction? 3 right? No way! That's wrong and that's wrong. How far to the left has it been moved? Darn right. It's that one. That one. A lot of kids that year picked this one because, oh, that's 6 to the left. No, it's not. It's 3 to the left. Nearly done. Almost there. Well, this here isn't transformations, but you just wrote a test on this. How many terms are there in that expansion? Give me a hint. Not 7. Right? When you foil a plus b all squared, you get the trinomial. When you cube it, you get a fourth or a quadnomial. Whatever you want to call it. Written section. So you're going to get something like this. That graph is graph below. Graph that. What's that negative they're going to do? Vertical reflection and 3 left. Are you okay on these? Hopefully not. Any specific questions you want me to talk about now is your chance. Otherwise, I think I've gone through the whole unit. I've done reciprocals. Done absolute values. Done inverse. I've yelled at you and scared you. So, any others you're thinking about? Best advice I have over the next few weeks start working through those provincial exams. If you run out and you need more, email me. I'll happily get you more. You have more. If you run out and you need more, email us. We have more. We have lots of review stuff. Here's the worst advice that I can give you. Put everything off and try cramming this in two days before the exam. Not the best way to learn. Not mentioning any names here. Are we done then? If you feel we're done, could you please turn in my little exam booklets there? At this table. We're going a week and a day from today. Tuesday after the May long weekend. We're going logs. That one I suspect will be a little more intense.


And you're back here on likeable science another Friday afternoon. I'm your host Ethan Allen. Thanks for joining us. And likeable science is all about how science is a vital, interesting, and dynamic part of everyone's life. We face the same kinds of challenges in science as we do in other parts of our lives, and we all overcome them too. And that's what we're going to talk about today. Joining me via Skype is Tanaia Valerie, who is a doctoral candidate in molecular physics and biochemistry at Yale University. Welcome, Tanaia. Hello, Ethan. How are you? I'm doing well. Very nice of you to join me. Thank you. Thank you for having me. So I had run into Tanaia through a column that she wrote. It was published in Science Magazine. There's a weekly column called Working Life, and Tanaia wrote about a column called Growth from Failure and talked about the struggles she'd run into with experiments not working and all kinds of difficulties and the frustrations and actually shame she felt about this and tell she sort of had a breakthrough and overcame that, began reaching out and getting some help from her mentors and some of her lab peers and has grown from this and become a better person and better scientist. Is that fair to say? Yes, definitely. That's where the growth comes from, right? Exactly. So I was so impressed by this because it harked back to an experience I had had as a graduate student when I realized somewhere in my about third or fourth year of graduate school that I gathered this mountain of data but I had been refining my techniques all along and finally was just going to have to throw all this data out and sort of start all over with basically now my finally refined experimental technique and it was very, very discouraging, but yes, we break on through these things. So why don't you tell us a little bit about this, Tanaia? Yeah, so this piece was featured in Science, so that's one of the top journals in our community and how it came about was that I reviewed, I wrote in about another working life piece and then I was corresponding with the editor and she asked if I had something to contribute and I said, sure. And so when we were talking, she's like, well, we really want to hear about turning points, you know, graduate student experiences that really change how you look at science or how you function at the lab bench and this was one of those crucial times. The time this piece was about one of the top most painful experiences that I had and the reason I chose to write about it was because I hoped it resonated with others. In fact, it took a lot, a lot of courage for me and I had to push myself to be really revealing about what happened because it was such a point of pain because it was a failure, I had failed but there was also growth and then I hoped to share that growth with everyone else and I would resonate with them. Yeah, absolutely. And it's an interesting point that people, as you commented in Type A, people don't like to admit that they are failing, they're having problems, they're reluctant sometimes to reach out, to ask for help and of course that you realize, of course, in your lab, you're surrounded by other people whose experiments all appear to be successful but then you realize they might just be hiding their problems, their failures from you. Just as you were trying to hide yours from them. Yeah, it's so much energy to keep up this illusion of perfection and what actually gave me courage to start asking for help or that sort of thing was actually paying attention more closely and seeing that my colleagues were in fact reaching out for help. So sometimes when we view the perfection in ourselves, we see it in others but when you start paying attention to what actually is happening around you, you might see that there is people asking for help and you just didn't pay attention. Right, you find that the apparently super talented superstar actually does have difficulty and they can't pipe out worth a damn or something like this. They're a terrible speller, whatever it may be. And fine, if you examine it, they are facing some challenges too. So do you find this has really now made a difference in your life? Are you now reaching out and trying to be more helpful to others? Well, I've always been very keen on helping others but for me what the turning point was that when I see myself creeping into that fear of failure and when I start closing up and not sharing what's really happening, I actually have this moment of like, okay, this is what's happening and we can't let this happen again. And what's positive reinforcement of that is that since I've started reaching out more and definitely being much more open about my failures during my weekly meetings with my lab, I'm very honest about, okay, I'm really scared about this coming out correctly or I say that lost sleep over waiting for these results but when I'm much more open, I've just gotten positive feedback back. It was just reinforced that if you're open, people are going to be open back at you and it's been a great experience because of that and I'm glad I've chose this way of talking about my science. Yeah, absolutely. I recall years ago being in a position in an organization and my boss, the Chief Operating Officer just sort of casually mentioned back when he got fired from this job and I was sort of taken aback. It's like, wow, this guy is saying I got fired from this job and I think I was very sensitive because I had shortly before been fired from the job and hearing him sort of told me, oh, this is okay, this happens to other people too. I'm not the only person who's been fired, right? And people live through it, they survive, they thrive, they go on bigger and better things, you know, and so that openness is very, as you say, it's sort of relaxing almost to do it. I agree because what's been a really cool, unforeseeable aspect of writing this piece is that people are reaching out to me. I had this fantastic email from a student, another graduate student who was going through a challenging time and he wrote to me saying that how he got courage or he was able to be more courageous in what was going on around him and his own difficulty in grad school because he read my piece and that's the sort of thing that you hope happens when you're open about these failures and it seems like that is a case in your situation too. It's got to be gratifying knowing that you're open like that has really done someone else some good and helped them survive a difficult time and make it through. So has this translated into other aspects of your life other than your research? Yeah, certainly. Besides the bench, there's other things that we do and one of them happens to be preparing for our career after we earn our PhD and so I'm talking about a kind of a student organization and postdoc organization at Yale where we work on networking and reaching out to people and working on software skills, business skills and so when I talk about some of the struggles that I had at first while I was learning some of these skills of networking that has been really helpful for some of the younger people that are joining and so yeah, I would definitely say that this sort of resilience and being open is applicable to any sort of aspect of your life and as we were talking about before off the screen we were talking about I have read books to help me get through these times and some of these books come from authors that are former Navy SEALs or someone that's also in a research position but you can get inspiration to overcome any sort of life struggle from other people that might not be scientists in the case for me everyone experiences these struggles.  Really I think this speaks to this sort of broader issue of and people call it different things people talk about collaboration people talk about strategic alliances people talk about friendship people talk about outsourcing and these things all to some extent can be the same sort of activities in the sense of reaching out and getting getting some help on some aspect that you may need where you find somebody who can do something better than you can do it more easily or more effectively and hopefully of course there's some reciprocity in the whole business, right? Yeah, collaboration is so key and that's the other thing that I've been really embracing is that as a community or in my case as a lab you work together to make things happen and it is so important and not only do you have to be willing to accept help that's number one but also just be grateful for it and then of course paying forward if you can't pay back you know you pay forward to help others and when you do that you just bring in so many different talents so for example we have a lab manager who works with sales reps to get our reagents at affordable price and if that person wasn't there and didn't have that sort of network I would struggle more on the bench and so having these key roles within the lab or any community is so important for keeping it all running smoothly in the end and then making it such a thriving environment for everyone to do well then it's actually really interesting I'm reading this book by Adam Grant and he's a professor at the Wharton School at University of Pennsylvania and in it was an interesting study with cardiac surgeons and also some financial analysts too and then what they found were the stars super outperforming stars of the cardiac surgeons that did really well and what they found was that if they were in a thriving environment that they actually had a lower incidence of death in their surgery they had nothing to do with practice like the common thought is that you practice to do better but also what he was reporting in the book was that the cardiac surgeons actually thrived and also depending on the hospital community there so it's important for all aspects I would say absolutely I've actually just been reading a little bit about Google's project Aristotle where they spent years actually analyzing what made it for a good team but I want to switch gears for just a moment here because we talked about persistence as part of resiliency and all and I want to tell one of my little campfire stories here a little peculiar science piece that perhaps will be of interest to some people this one is something I only recently ran into there are a little caterpillar that eventually becomes a moth they're called the woolly bear caterpillar I think that's the name that's applied to a lot of different caterpillars actually but the ones that live in the Arctic face a peculiar challenge these little caterpillars have a very very short time only a few months of the year when they can be active and as a caterpillar you have one job that's to eat a lot of food as fast as you can to get the energy to turn into a butterfly or a moth and there simply is not enough time from the time these things hatch until the upcoming fall for them to get enough food so come fall the woolly bear caterpillar crawls under a rock basically and then as winter sets in they freeze they freeze absolutely solid the rock is buried under snow the woolly bear caterpillar's body is completely solidly frozen and come spring everything begins to fly out and eventually the woolly bear caterpillar falls out and resumes eating and proceeds to keep eating even as fast as it can and it doesn't just do this once or twice these things go through 14 years 14 cycles of freezing and thawing for 14 years before finally one summer they had finally eaten enough that they are now ready they pupate and then they pop out as a moth live for a few more weeks and die but I thought it was one of the most amazing things I had heard in a long time and again it just I think it ties in with this whole business of persistence these things put up with being frozen solid 14 different times in order to sort of make it through their life and get to where they need to be anyhow on that persistent note we're going to take a short break here about a minute break and I'm talking with Tanya Valerie, a doctoral student at Yale and we're talking about setbacks turning into success we'll be right back I pity the fool who ain't watching this show at 12 o'clock on Friday afternoon Stan, the energy man, watch it I'm Jay Fidel and I'm here with Pete McGinnis-Mark to talk about HIGP and research in Manoa what about that show Pete? I think it's great Jay research at Manoa really provides faculty members at the University of Hawaii with an easy way of explaining some of the research activities we're conducting on the campus for example I do a lot of space research whether it's the moon and Mars but many of my other colleagues do other interesting kinds of work whether it's exploring the ocean floor in submarines studying earthquakes and tsunamis or other activities so research at Manoa really provides us with a way of telling the general public some of the activities which we're involved in as well as communicating to our colleagues and students this is a fun science and we really appreciate the activities which research at Manoa enable us to talk about I love research at Manoa come around, join us it's Monday, one o'clock p.m. every single Monday be there, we'll be square and we're back here at likeable science I'm your host Ethan Allen joining me today via Skype is Tanaia Ballery she's a doctoral student in molecular molecular physics and biochemistry at Yale University and Tanaia wrote this wonderful column in the working life weekly column in science published called growth from failure in which she very openly and honestly discussed her setbacks, her struggles, her failures and what this meant her emotionally and how she's worked through it and has grown from this and learned more to reach out to seek help when she needs it to look at other people for advice and assistance and it's great but there is a whole issue of course you can't just do this randomly you have to have the right people around you and of course you're working in a research lab where the head of your lab presumably has rather carefully selected folks and hopefully a good balance of people with complementary skills and personalities that don't create too badly at least because as you pointed out you have to have a good collaborative team there because you're all working on closely related projects you're doing supports some of your lab mates and their work supports yours and the PI is trying I assume to tell a particular story Yeah, definitely I would say my PI does an exceptional job in putting that in and that's something I hope to learn from her a skill of hiring someone from one interview or two and get to know who that person is and see how they would fit in your team and how they would thrive and what I've seen and this is with working with students as a graduate student we also teach and we teach undergraduates so for me that would be Yale undergraduates and it's interesting because when you approach these sort of situations where it can be difficult and challenging you often see the strongest characteristics of the people around you and what's really important is that everyone gives and gets back and is supportive of each other and tries not to judge each other and so I think those are really important characteristics to have in the team that you're working with but also the team that may be under you or even above you the leadership team and it's an important learning experience it's not something I appreciated when I was younger something that you kind of have to live That's intriguing to hear you say that because this is exactly what this project Aristotle found is that people have to make a good team people have to feel psychologically safe they have to have an environment where they know they can express their ideas freely and they're not going to be judged or laughed at or made fun of they've got to be able to share and communicate it doesn't work if one team member talks all the time and another never talks actually the amount of talking it turns out among team members has to be pretty much equal over the long term for teams to be successful and then the other thing they brought up is that the most effective teams have people who score very high on empathy ratings people who are very good at reading other human beings reading facial expressions, reading body language those are people who typically when you get a bunch of them on a team your team works quite well because they didn't have the other team members or feeling and can react more appropriately whereas people who are not empathetic will run roughshod over at a time when you're trying to reach out for help and they won't see it or hear it and may not respond appropriately and that will of course discourage you then from Yeah, I completely agree and there's even this fact where you kind of have to you know, you have to forgive your other teammates because sometimes we get really excited about the science and so someone might be really energetic and this is where criticism might seem harsh or negative, really negative but what's important when you're receiving that too is to remember that and if luckily if you're in that environment this is really important you have to have that trust already but you know that that person is coming from a good place and as you mentioned having empathy is a great characteristic and I've experienced this where another team member will come in and kind of smooth it out if one team member is really energetic about giving their criticism and maybe not be conscientious of how harsh they're coming across even though they have really good intentions sometimes it's really great to have that third person coming in saying, okay, you know what she's doing is really great and this is the focus that she needs to go in and kind of help bring because we're all human, we all make mistakes and I think working as a team it's so crucial in so many ways, yeah Absolutely and that willingness to understand that the other person well, it sounds like they're criticizing you harshly may not mean it that way they may be trying to be very helpful to you and just sort of stylistically they're sort of blowing it and yes, if you're lucky there's a third team member around to sort of mediate the whole thing tell the criticizer to tone it down a bit and highlight some of your good stuff too, right? But if there isn't, you just have to be able to do something that yourself and realize, no, this person, yeah they don't only mean to be this way they're just coming across that way so that's again why it is important to have good people around and to sort of choose your team members well and carefully, right? Because, yeah my wife likes to say she says, I love working with smart, good-hearted people and she says, I can work with dumb, but good-hearted people because they're good-hearted and you can get past things and I can work with smart, bad-hearted people because if they're smart, again you can help them see why they need to do it this way but she says there's no future working with dumb, bad-hearted people, right? Just give up on them right away, you know? They're not going to be good teammates Yeah, and that's something that I've also come to appreciate a good leader also needs to recognize when a team isn't working, right? Because we talked about how collaboration is so important, but sometimes you might not really get the good sense or like the right sense of someone and then knowing when to, you know call it quits too and knowing when like that interaction isn't working can also be a valuable skill. Yeah, and it's funny because scientists and scientists' training does not typically train them in those sorts of arts to be able to spot subtle human interactions to be able to be good empathizers and so it was interesting what you were saying earlier that you think your lab head is amazingly good at pulling people out after even a brief interaction and realizing if this person will work or won't work in your group and that is undoubtedly a valuable skill but it apparently is a skill too that can be taught a bit like the other, but Yeah, this is actually something that I think we need to work on in graduate student education. We need to have a course in this and how to manage a lab, right? Personnel, human management human resources I think is the official term and it is something we need to work on to incorporate into our education because as we've been talking about through this, our conversation is that an effective scientific team and this is true for any sort of discipline but definitely true for science that they're to thrive and do really well and ask really interesting questions that push the forefront of science forward and our knowledge base forward that you just, you have to have that, you know, and they'll take it for granted. Right, but it's true, I mean more and more and all the studies that are being done in the business world now suggest that more and more of our work is done in teams and less and less are we working on our own and therefore this idea of teamwork is more and more critical and yet again in our traditional schooling we don't typically do much of this at all we take, you work alone by yourself, you take tests by yourself you're not allowed to ask for help on some kind of assignments and so we don't get a lot of practice in it and you're right I mean sometimes working in a science lab is the first real experience of real sort of close collaboration that some people have and yes, I agree I think you should suggest that to the Yale administration they should do Yeah, I'll have to mention it to them Yeah There's so many other things too that we would need to learn but yeah, maybe even like a course in empathy as you mentioned would be great for us That would be a key aspect of the good teamwork above and beyond the communication skills and I used to do a little bit of that was working on graduate students with their communication skills because I have learned that it's all too easy to drift back into scientific jargon and so I used to when I would be at a party early in my graduate years and people would say, oh what do you do and I'd say well, I'm using upper and conditioning paradigm to study the photopic and scotopic spectral sensitivity of the African cyclic haplocromus brutonii and people were usually asleep or they wandered off by the time I got through that and I learned after a while to say instead I train fish There you go and that was much more effective way to communicate because immediately the questions would start flowing people, why do you train fish how do you train fish, what are you training them to do and the conversation flow and communication flourish so I learned that trying to simplify things down can be a very powerful thing and I used to work with the doctoral students at UW to train them to tell about their work in more accessible terminology and I think something because I can only speak from the scientist side and I know we're talking to an audience that might be able to know what makes this but we scientists actually really care that everyone knows what we're doing because we love it so much it's our passion and when they don't get it they have that starry-eyed look like oh yeah okay wow that's really cool but that's not what we like we actually like interacting with people and talking about our research because not only is it our passion and what drives us but we want other people to be enthusiastic too and for my case you're studying fish so I study RNA molecules and I think it's really cool how their structures work and how that goes toward how they function in a cell how they make things happen and it's just it's so important I'm so glad to hear that you're teaching these graduate students how to do it properly and I just want everyone to know that we actually do want we scientists, the scientific community really care about sharing our interests right I mean this gets back to Einstein's famous dictum that you really don't understand something well until you can explain it to your grandmother you know it is true well hey this has been a wonderful conversation and I very much appreciate your being on the show and sharing your very likable science and your very likable approach to science with me here and with our viewers and it's certainly I feel like I've learned a ton from you and that's that's always great I always feel like that makes for a good show I hope it's been a good experience for you and I hope perhaps I'll get you back at some point and you talk further thank you I appreciate that it's been a true pleasure to talk with you and I look forward to interacting with you more and I've certainly learned a lot too about what you said about the group Aristotle yeah really interesting so Tenea Valerie, a doctoral student at Yale University has been with us today and I hope you will come back and join us next week on likable science


This study investigated the safety and efficacy of oral phage treatment in children suffering from acute bacterial diarrhea. The results suggest that oral phage treatment may be safe and well tolerated, but it does not appear to have any significant effect on diarrhea outcomes. Further research is required to better understand how phage treatments work in the human body and what factors influence their success. This article was authored by Shafiqa Alam Sarkar, Shamima Sultana, Gloria Rudler, and others.


There are many releases for the month of March when it comes to Manga, but I am here to show you 20 of the most anticipated releases that I think are worth checking out. Let's do it. We have another chaotic month of new Manga releases. I try and limit myself to just the volume once, like I always say. It's kind of easier to recommend new series instead of telling you to buy a volume 40 or 20 of a pre-existing one. So with all that said, let's get started. We begin with a trio of Kodansha releases. The first book that we're going to talk about is Eidu or Ado Volume 1. This is a Senen Manga written and drawn by Amano Jaku. This is a sci-fi futuristic story, but it also deals with very humanistic themes. We follow a wave of immigration. Japan has become a volatile mix of people and cultures, brought by the protest of xenophobic extremists unhappy with the new status quo. A brash, job-hopping young woman named Riko is driving her scooter through one such protest when she sees a boy about to get run over by a truck. Riko just manages to shove him out of the way, and in the hours that follow, she finds herself looking after the boy named Eidu. Riko takes Eidu out for a bowl of ramen, but just as they're about to dig in, Eidu is fired upon by a distant army sniper. As the bullet pierces the restaurant window and comes whizzing towards Eidu, plant-like tendrils snake out from his arm and stop it mid-flight. Who in the world is this boy and why is the army after him? So obviously this has very Akira vibes running throughout, and of course cyberpunk themes and dystopian futures and stuff like that, so I'm very interested in reading this. It is currently ongoing, so I cannot tell you how many volumes it's going to be, but it looks pretty cool, and I do want to check it out. I love the mixture here of social commentary, a little bit of politics, a little bit of futuristic sci-fi stuff with what I assume are supernatural abilities. Next up we got a shoujo manga, this is anyway I'm Falling in Love with You Volume 1, also being released by Kodansha, like I mentioned. This is written and drawn by Haruka Mitsui. This one tells the story of Misuha in her 17th birthday. Her parents totally forgot about it, and the senpai she likes isn't interested in her, but when her long-time childhood friend asks her out, Misuha has to sort out what this change could mean, and her feelings may not be the only ones changing. Adding to the challenge is a global pandemic appending the hopes and joys of high school life, but romance is resilient and crushes and confessions flourish among Misuha's friends, a brand new love story from the author of I Fell in Love After School. It's interesting to see the theme of a global pandemic, I'm not sure how that will function within the story, but it is nonetheless interesting and I'm willing to check this out, I do like the art being displayed here. Next up from Kodansha is one of the most anticipated releases, Metalist Volume 1. This is written and drawn by Surumaikara. This is another Saiyan ongoing series, and this one has a prestigious honor to it. This won the 60th Shogakugan Manga Award in the general category back in 2023, so you know it's pretty popular. This one is about figure skating. Inori is a little girl who dreams of becoming a figure skater, yet the obstacles to this dream feel insurmountable. Inori is already too old, she's 11, she's always had trouble at school, and worst of all, her older sister's skating dreams ended in failure, so her mother is dead set against putting her other daughter through a similar experience. Still, the rink is the only place Inori can be herself, and she's out on the ice when a fateful meeting takes place. Tsukasa, a frustrated coach on the edge of giving up competitive skating himself, will join Inori to form an unstoppable duo powered by hard work, transcendent joy, and an unshakable belief that they can prove everyone wrong. Just by me reading that description, I can already tell you why this thing won an award. It sounds great. I love the inspirational story here with these characters fighting against old odds to prove to themselves and to others that they still got it, that they still want to venture forth and make their dreams a reality of being in this competitive sport. I'm not big on figure skating, but sports stories have always been really good. You have the highs and lows, you have the drama, and the whole competitive nature that make for some compelling storytelling. So definitely be on the lookout for a medalist Volume 1. From Love Love, the imprint of Tokyo Pop, we have Cover My Scars With Your Kiss, Volume 1, written and drawn by Iyo Amaki. This is a BL series that ran from July of 2019 to 2020. Seiichi Kurosu is the handsomest eldest son to inherit a large company. After running into insecure dentist Nao Seto not once, but twice coincidentally, Seiichi wonders if fate is at play. When Nao reveals that Seiichi actually reminds him of the man he's been in love with, Seiichi proposes a deal with him. From the length of time he receives his dental treatment from Nao, the two of them will date. Nao's tragic love story combined with Seiichi's status as family heir and the impending countdown can something good come from such a relationship. I'm not gonna lie, this sounds really interesting. It's a nice juicy drama story, so yeah, if you are into BL stories, definitely be on the lookout for Cover My Scars With Your Kiss. From Square Enix, we got The Villainess's Guide to Dot, Falling in Love, Volume 1. This is written by Toya with art by Ren Sakuma. This is an ongoing shoujo. From a mundane existence to an extraordinary adventure, Luciana, once an ordinary woman, now finds herself reincarnated as the stunning villainess of an otome game. Well aware of impending plot twist, she's ready to rewrite her destiny and avoid catastrophe. She hatches a brilliant plan to live a peaceful life and avoid troublesome suitors. What could possibly go wrong? Surprise! These persistent men refuse to take a hint. And if that weren't enough, she also possesses incredible, unparalleled magical abilities. What about this world has made her so special? From Titan Manga, we got Tengen Hero Wars, Volume 1. This is written by Yasu Hiromoto with art by Kubaru Sakanoichi. This is a Senen historical Isekai military series that is still ongoing. After receiving a mysterious invitation to come play in heaven, Oda, Nobunaga, and his sister are transported to a mysterious new world where the mightiest warriors from history will meet to do battle. Here the pair will meet legendary figures such as Napoleon Bonaparte, Julius Caesar, Zuge Liang, probably butchered that, sorry, and plenty of others to see who will be crowned the greatest of all time. Obviously this is very reminiscent of Wrecked of Ragnarok, only the stakes aren't as high. The rest of humanity is not at risk, except the main protagonist here on this book of Tengen Hero Wars. So we'll see what happens.  I couldn't share some of the panels that I saw because they were brutal, and I don't think the YouTube algorithm would appreciate that. From Vizmenia, we got a double dose of One Piece. We're getting One Piece Shokugekino Sanji. This is written by Yuto Sugura in art by Shun Saeki. If you don't know this creative team, they are the ones responsible for food wars. It tells of the straw hat chef Sanji as he dishes up in his battle to win over the bellies and hearts of all he feeds, man or woman, friend or foe. This one-shot spin-off rolls all six original story chapters into one collection. This is a collab made in heaven.  The other One Piece spin-off that we have here is, of course, Ace's Story Volume 1. This is written by Sho Hinata and Tatsuya Hamazaki with art by Boichi. This is a spin-off of the One Piece franchise detailing Ace's story collected across six chapters or two volumes that ran from September of 2020 to December of 2021. Readers can follow the story of the man who lived like a wildfire. From the moment he formed the infamous spade pirates, discover the daring, paradical feats of Firefist Ace, straw hat Luffy's legendary older brother. So, similar to the previous book, if you're a fan of One Piece and, of course, the character of Ace, then you are getting this book, right? Another very interesting release, and it's not for the reason you might think, this is number call from Kodansha. This is a one-volume series, one-and-done volume, as I like to say, six chapters that ran from 2013 to 2014. This is written by Nagisa Furuya, and it is highlighted here that they are the creator of My Summer of You series. High schooler Eito Tachibana has always hated his name, including all of the jokes and puns about the number eight that have come along with it. It's as if the number has haunted him like a ghost ever since he was a child. One day, he meets a classmate named Tomoya Hata, also known as Hachi, the Japanese word for eight. What begins as casual greetings and small talk in the hallway soon becomes something much deeper, and Eito realizes that it's more than just a similar nickname that draws him to Hachi. Could the number that Eito resented for so long finally bring him something he'll love, and is that someone Hachi? Now, I had another manga listed in here that I wanted to recommend because it was a kuma release, and I had never talked about kuma on these videos before, and I'm open to talking about everything on this channel. All manga are valid, I appreciate all genres and topics and all that fun stuff. Everybody out there has a book waiting for them, and who knows, that book might be it for some people. Unfortunately, I've been adding, as you're seeing in this video, preview images for these books. I've always wanted to do that, and well, here we are. It took me a while, but I'm adding the previews. And when I looked up previews for that manga, it was just way too spicy. And I'm not joking. All the images I find, I cannot show. So I didn't want to do that and leave that one hanging. So here we have Number Call instead, and it just so happens that I really enjoyed the description here. I love the wordplay and the theme surrounding the number eight. I think it's pretty clever, and it sounds pretty dramatic and sweet at the same time, so heck yeah, I'm going to recommend it as well. So go check out Number Call from Kodansha. From Yen Press, we have The Tiger Won't Eat the Dragon Yet, Volume 1. This is written and drawn by Hachi Inaba. This is a Senen fantasy series that is still ongoing. In the mountain somewhere, a tiger catches its prey, a lone dragon, the kind that is hardly ever seen. Eating the dragon's meat extracts the ultimate flavor. Drinking its blood heals all one's injuries, devouring its heart grants immortality. And yet upon seeing the dragon's undeveloped stature, the tiger refuses to eat it. Dragon and Tiger, predatory and prey, is what ties them together. Simply natural hunting instincts or something more. I'm not going to lie, suspicious looking covering aside, I'm actually really intrigued by this. I like the idea that this story is out in the wilderness. There are no humans. You get essentially anthropomorphic animals, but they have real animal forms, and I like the whole premise of, you know, these characters inhabiting human traits as they start to get to know each other and break down barriers for peace and love. I say with air quotes that I'm doing right now, but you can't see them, so don't worry. I do like the art from Hachi Inaba, so I am eagerly anticipating to read this. No joke. From Seven Seas Entertainment, we have a GL ongoing. This is How Do I Turn My Best Friend Into My Girlfriend, Volume 1. This is written and drawn by Siyu Yasaka. Minami and Yuzu have been besties since, well, forever. Or at least that's what Minami thought, but when some rando confesses to Yuzu, Minami realizes that her feelings might not be what you typically call friendship anymore. It doesn't take long for Minami to realize that she wants to change their relationship status, but will she be able to muster the courage to confess? Or will she simply be happy being by Yuzu's side?  Interested to know if you guys are going to pick up How Do I Turn My Best Friend Into My Girlfriend? Let me know in the comments section below. Black Summoner Volume 1. This is a long-running series that started as a light novel, and if memory serves me right, it is still ongoing, so we are finally getting the physical edition of the manga being published by J-Novel Club, JNC. This story is written by Dofu Mayoi, an art by Gin Amo and Kurogin. Digs. I don't know if I pronounced that correctly, but I'm gonna go with it. Apologies in advance. This is an ongoing Shonen series, by the way. A boy finds himself in a strange place with no memory of his past. His name is Kelvin, and he soon discovers that he's been transmigrated to another world, giving up even his memories in exchange for extremely powerful abilities. Thus, he begins his journey as the world's strongest summoner, challenging one mighty adversary after the other, gathering allies and discovering his calling as a true battle junkie.  From Yen Press, we have a very unusual release, but I am really interested to read the story. This is Adult Picture Book New Edition Volume 1. This is written and drawn by Kay Itoi, and it recently wrapped up. This is a Senen series. It ran for three volumes, 21 chapters, from December of 2021 to July of 2023. Erotic manga author Kudo's friend Haruki passed away, leaving behind his young daughter Kiki, and a note bequeathing her to Kudo. Strange as the situation is, Kudo commits to making a real family for the girl, so when he meets a woman who reminds him of his late friend, he fires off a marriage proposal on the spot. By blood, friendship, love, or circumstance, family is family. I'm interested in finding out if Kiki will discover her late father's work and what is going to be her thoughts on the subject. I can't be the only one that thought of that, right? Or maybe that's just me, maybe I'm just the weird one out there. Regardless, we can find out now, thanks to Yen Press releasing this volume in the month of March. Another release from Kudansha is I Can't Say No to the Lonely Girl Volume 1. This is Story and Art by Kazikaze. This is a GL series that ran for six volumes, 34 chapters, back in October 2019, all the way to October of 2022. Quintessential good girl Sakurai finds herself trapped in the middle of a bribery scheme. Her teacher offers to write a recommendation letter in exchange for luring a truant student into attendance. Sakurai pins down the reclusive transfer student named Honda, but there are strings attached. Honda demands that Sakurai grant one wish every day. The first wish is a kiss, and Sakurai finds herself feeling very eager to please. From Viz Media, we have Magin Lumiere, Magical Girls, Inc. Volume 1. This is written by Seika Iwata and art by Yu Aoki. This is a currently ongoing Shonen series, but if you're not sure about it, I got some alternatives for you because I think this series is about to blow up in popularity. There's never a dull day at the office when you're a magical girl. Are you looking for something new, something challenging, something very highly paid? Exterminating monsters is an exciting, fast-paced field that will get you out from behind a desk and into the action. With over 500 magical girl companies now in operation, you're sure to find a position and uniform that fits. Start your career as a magical girl today. Kana Sakuragi is an excellent candidate for the job. Any job she's motivated and organized, and has a fantastic memory. So why has she interviewed at over 15 companies without a single offer? She's trying to keep a positive attitude, but it seems like her bad luck is only getting worse when a monster crashes her latest interview. As Havok ensues, she finds herself helping the magical girl who comes to their rescue and ends up with more than just her life in return. Meet the newest magical girl at Magin Lumiere, Magical Girls, Inc. That's a long description, but if you're still unsure about this quirky, awesome premise, I got two solutions for you. One of them, you can actually read this series for free, legally, at the Manga Plus website. This is not an ad, I just like using the website and I want you to use it as well. So you can read most of the chapters there for free and get a good feel for the series if it's something you want to own physically.  This is getting an anime adaptation for the spring season 2024, so it's right around the corner and I'm pretty sure you're going to stream it at one of the popular streaming sites. So there are multiple solutions for your magical girl dilemma if this is up your wheelhouse. I'm going to check it out, the anime, and I'm going to pick up this volume eventually, so count me in for Magin Lumiere. From Yen Press, we have I Want a Gal Gamer to Praise Me, Volume 1. This is an ongoing series with story and art by Geshu Maru. When a high school Shiren Raito Sasaki hires a pro gamer coach to help hone his FPS skills, he never expected that the one knocking on his door would be Rion Suzuki, a cute and fashionable beauty the same age as him. With such a charming and supportive gamer gal cheering him on, can Raito take his game to the next level or will the pressure of being up close and personal with a bombshell like Rion lead him to throw? First of all, I like that there's no weird creepy age gap and they're all in the same age group. That's awesome. Also, I am an old school retro gamer and I've never needed a coach to help hone my skills. But then again, I don't play FPS's and I'm not in the competitive scene, so what the heck do I know? I'd rather play arcade games and platformers. That's just me. But still, I like that it's a gyado from the looks of it and the mashup should be hilarious. So if you're interested, go pick up I Want a Gal Gamer Volume 1. Is it Dejavu? No, it's Initial D, the first omnibus edition. This is one of the most anticipated releases for the whole freaking year and it's finally here. Kodansha is putting out the omnibus edition, Volume 1 collecting Vol 1 and 2 in a large-sized 2-in-1 edition with a refreshed translation featuring story and art by the legendary Shuichi Shigeno. This Saiyan Classic series is finally being collected after being out of print for so long at Tokyo Pump and we're getting the whole shebang. That is awesome. All 724 chapters, which was 48 volumes, so now it'll be 24 volumes total to collect this series.  If you don't know about Initial D, this tells the story of Takumi Fujiwara, who spends a lot of time behind the wheel. His tofu delivery job sends him racing down the treacherous roads of Mount Akina and without even realizing it, Takumi has mastered racing techniques that most drivers take a lifetime to learn. Of course, none of his friends realize this. They're all too busy watching the local street racing team. When the legendary Red Suns show up to challenge the speed stars, the rival team obsesses over a phantom car, the Trueno 86 seen racing through the mountain roads. Who is the driver and will they take on the dangerous challenge? Also, I do want to point out that since this is such a hyped special release, there are multiple variants for this release. You got the standard cover and depending on where you shop, you can get a DM direct market cover on places like the crunchy roll store, in stock trades, etc etc. Or if you go to Kinokuniya, you can also find a special manga cover as well. I am so happy that this is out, reprinted with a better translation. Count me in. Even though I'm not into racing, I still love Initial D and I can't wait to have this on my collection. From Kodansha, we have a pretty wild release. This is I got reincarnated in a BL world of big man boobs volume one. This is written and drawn by Tsukiji Nao, shown in BL series. I gotta read the full description because it's hilarious. The first line in my script here says, I just wanted to touch boobies. If you're not intrigued by this already, I don't know what's wrong with you. Nagare Otokawa was an otaku loser, obsessed with press. He tragically died never knowing the feel of the sweet, sweet bosoms he craved all his life. Little does he know, his wish is about to be granted in a way he never would have expected.  Even so, he sets out to find and squeeze the bust of his dreams. He does in fact end up with his face planted deeply in some luscious cleavage. But to his dismay, it's the magnificent pecs of the super muscular class delinquent, Ryuji Onizuka. Now Nagare must try to dodge his way past the barrage of BL scenarios that hurtle into his path. Will he persevere and get the busty girlfriend of his dreams? Or will he end up falling for the all-man yet temptingly bodacious Ryuji?  That is the official description, and it sounds amazingly ridiculous, and I want to check this out. So if you're excited for the world of big man boobs, leave a comment down below. Leave, I don't know, balloon emojis if you got it to this part. Pretty excited to check that out if you're in the comment section. We got another release from TitanManga. This is Grace Rosa, Volume 1. Now there's something interesting here, because to my understanding, and somebody can correct me in the comment section, this Saiyan series written and drawn by Himuro got discontinued or cancelled back in 2020. It only ran for six chapters and only one volume was released. So I don't know what the plan here is. I don't know if the plan on splitting things up three and three, or if this is a typo and it's meant to be a one-and-done volume as it should, but it is officially labeled as Grace Rosa, Volume 1. Grace Rosa is an assassin driven by a single thing, discovering the secret of her adoptive father's disappearance. He trained her to become a lethal killing machine able to wield any weapon she can get her hands on, before inducting her into the ranks of the shadowy organization known as Alterna. But could the very people she serves as a hired gun have something to do with him vanishing? And to what lengths will she go to enact her vengeance on the people who have wronged her? From the descriptions that I've read, this is great if you're a fan of the John Wick series. You will be right at home with this type of storytelling. The art looks extremely brutal. I had to look through other official previews to post here, because yeah, some people were blown off and blood and guts and brains all over the place, so not the kind of thing I want to highlight on this video, but if you're interested in that level of assassin gunplay violence, then you'll be right at home with Grace Rosa. Finally, we close out this wild and wacky anticipated releases video with a Yen Press book. The Alchemist Who Survived now dreams of a quiet city life, Volume 1, Cycle of the Elixir. This is written by Aya Obada, an art by Usata Nonohara with Ox. This is a manga adaptation of a light novel of the same name, however, this happens to be a reboot of the manga. The first one came out back in 2019 and it was cancelled with two volumes out, and they're still available. You can purchase them online, do not get confused, follow this guideline here with the cover that I'm showing. This is a new reboot, ongoing as of 2020, and it tells the story of Mariela, who performs incredible feats of magic, so when a stampeding horde of monsters threatens to devour the kingdom of Endalsia, she decides to put herself in a brief state of suspended animation to survive. Luckily, she awakens safe and sound 200 years in the future. Now all Mariela wants is a quiet, laid-back life in this land she barely recognizes. It's too bad potions have become a luxury good and she's the only girl in town with the skills to make them. I love this premise, and I can already tell that I'm going to be frustrated with Mariela because she wants peace and quiet, but she's got the skills to make the potion, so it's not going to be peaceful nor quiet. It's going to be hectic and chaotic as people will try and get her to make these potions, but thankfully she has a way to earn some money, so that's good. So there it is folks, we have arrived to the end of this video. 20 anticipated manga releases, I hope you're excited for these, and if you're not and you're excited for something else, well leave a comment down below. I'm interested in finding out what all of you are getting in the month of March. Thank you all so much for liking, commenting, subscribing, and being part of Manga Geekdom. I truly do appreciate it. Thank you so much. That's going to be it for now. God bless. Stay safe out there. I will catch all of you on our next video.


Hello and welcome Speedway fans to LandShot. You join us for Race Off 1 of the FIM Monster Energy Speedway of Nations. OK, well we've got a little bit of an update. Practice has been cancelled, the FIM jury have decided due to the weather conditions that practice will be cancelled but racing is very definitely still on. So if you are local tickets will be available from the box office from around about one o'clock and if you want to keep up to date with everything that's happening down here it's across all of our social media on Speedway GP.


Under Secretary Dardas, GPFI, co-chairs, ladies and gentlemen, I am really honoured to address today's forum and I regret not being with you in person. First of all, as an honorary patron of the GPFI, I wish to thank Turkey for its outstanding leadership of the partnership and the continued commitment to financial inclusion. In just over two weeks, the United Nations will adopt an ambitious new sustainable development agenda which will set the stage for development efforts over the coming 15 years. The new sustainable development goals recognise that providing financial services to the poor is a vital means of achieving key development outcomes such as hunger eradication, poverty reduction and economic growth. This recognition shows that the issue has really come of age. We have come far in the last few years. The World Bank's Global Findex last year's survey reveals that while two billion people remain unbanked, 700 million previously excluded adults have been drawn into the financial system over the past three years, a remarkable 20% improvement. Having 700 million new participants in the form of financial system in just three years tells me that financial inclusion is a challenge we can successfully meet. However, the process is complex and it requires creativity, greater public-private cooperation and persistence. The progress we have made is in large part thanks to the private sector, cutting-edge products refined by continuous innovation are spreading financial inclusion faster and more evenly than ever before. So we must ensure that the private sector's contribution is harnessed fully during future G20 presidencies. Today's gathering is an important element of that process. Progress remains uneven among multiple populations and regions and this presents a pool of untapped potential. Women have benefited but not enough. Youth too face significant exclusion, this on top of the uncertainty of jobs they face in many countries. We owe it to the young people to provide them with the financial services and education they need to start their adult lives in the best way possible. The performance of small and medium-sized enterprises is also critically important. Too often these businesses remain cut off from credit, insurance, payment and other financial services. To sustain the advances we have made in financial inclusion, we must work to provide small businesses with the financial tools they need to become powerful engines of growth and jobs. Finally, as you work on these issues it is important to think about ways to further strengthen sustained private sector engagement with the GPFI as is suggested in the draft strategy. The Turkish presidency has chosen its priorities well and I will continue to extend to them every assistance I can. I am really confident that all of you will do the same in any way you can. Thank you very much.