Okay, what I really want to talk about today is explanations and let me start first by explaining who I am My name is Russ Olson. I work for a company called relevance. It's headquartered in North Carolina I live in Virginia where it's very humid and I'm now here where it's very not I've written two books and I'm working on a third and I hope you will buy many many copies of them But I didn't always start out as a as a programmer. It's funny. We all raised our hands yesterday Who has a BS in computer science? I have a BS in mechanical engineering And I started there. There's a few refugees and I so I started out doing things with gears and bearings and you know that kind of stuff and One of the things one of the things I found frustrating about that was you were always up against limits There's always a limit in mechanical engineering. There's friction on the gears The bearings will only take so much weight and then they'll fail Your heat engines are only so efficient and so you get equations like this Which are just all about the limits of what you can do in particular that middle one Which is the efficiency of a heat engine is Built into the fabric of the universe It's one of the fundamental laws of physics and there's no getting around that and I was really frustrating Because I always felt like there were things I wanted to do but I couldn't do them because there were these limits and so I wandered in the computer programming and One of the I mean I Guess one of the attractions was I didn't feel even a long long time ago when I first started that there were the same Kind of limits that there are mechanical engineering So I'd like to start with the question, which is what are the limits to what we can do? Right, we do all kinds of wonderful stuff, but we can't do nearly what we want to do What are the limits? Well, I could think of one possibility There's something that might be limiting us Or maybe it's guys in funny hats Or maybe it's these three guys But you know what I think it's all of us We make things out of ideas our tools are abstractions our raw material is data Right. Yes. We have you know the CPUs are only as fast as the CPUs are there's only so much memory and only so much This space but in the end the thing that limits us is Ourselves the thing that limits what we do is what we have up here in our heads And you know you sat through yesterday afternoon where people were talking about struggling to learn the things that we do That's the limit Okay, and I want you to just think for a second About what the world would be like if we were all just a little bit smarter Okay, if we're all just five percent smarter if we all just knew five percent more than we do right now What could we do? Well, the only way that we can get smarter is To explain things to each other Okay, you all know stuff, right and you all know different stuff and I know some things and the only way We can get the stuff the information from my head in the your head if it's at all difficult is to explain it Right, and I'm not talking about you know what I'm doing here is the least important kind of explaining That can be done It's the least important because it doesn't happen very often the important kind of explaining is the stuff that you do When you're walking down the hall and you get a co-worker and he says or she says how does this work? And you tell them that's the important kind of explaining because if you get that right You get that right then They'll be more efficient at their job and they'll make your company better You know we think of like If you're in a startup and you're doing a sales pitch we think of that as sort of sales. That's not sales That's explaining you are explaining why someone should invest in your company or how they should buy your product That's the important kind of explaining. How does this work? What does this function do? How does this class work? It's that day-to-day stuff just the overwhelming volume of it That is the important explaining that goes on. So what I'd like to do today is Talk about five ways to make your explanation stick that have good explanations Explanations that actually work because there's actually sort of an art to explaining things so number one Number one is to take it seriously Need to take explaining seriously why well because to do the right kind of explaining and as I said you can almost change the world Right, you could certainly Make your your the systems you're working on better make them easier to sell So we need to take it seriously and when technical people take things seriously There's only one thing they do They have a plan Okay, if you think about who we are and how we go about our lives We don't do anything without a plan Okay, if you think about what agile programming is Agile programming is both the most important advance we've made and I don't know 15 years and how we do what we do and It's also it can be boiled down to stop over planning everything Okay, stop planning and actually do it when we take something seriously. We have a plan unfortunately There's a default plan for explaining things the default plan comes to you courtesy of this guy That is James Joyce James Joyce wrote these long stream of consciousness completely incomprehensible novels and his plan is the default plan for an explanation. How does the system work? Well, let's see. I start talking about the last thing I worked on or the first thing or the part I like best or the part I like least the last bug I fixed the first bug I fixed Right, not the important stuff. Just whatever happens to be boiling around in my head. That's James Joyce stream of consciousness kind of Explanations and I really work very well a Better plan is the zoom the zoom in plan Okay, start with the big picture and you work your way down to the little picture because explaining is not just Information it's information with sort of a candy coating of context that helps people get the information into their heads okay, and By zooming in by using the zoom in plan You can supply the context. So what's the zoom in plan? It's pretty obvious You start with the big picture and you go to the little picture start with the earth and work your way down to the theater Beautiful theater here today How does this it yeah, what are we doing here? Well, we're trying to get filthy rich We're trying to build this e-commerce site. We need a shopping cart. We need the screen to be part of the shopping cart It's as simple as that okay the greatest top-down Context setting big picture to little picture Explanation that I can think of comes from this guy Abraham Lincoln The most famous speech in probably US political history Starts with these words and we tend not to think about them, right? They were drilled into you in fifth grade if you went to school here But if you think about what he's saying here, he's saying 87 years ago the country was founded the United States was founded So he's starting big picture. He's starting with the beginning of the country Now we're engaged in a great civil war. What's been going on in the last few years? We're here to dedicate a cemetery here this afternoon. It goes from the beginning of the country To what are we doing here today in three sentences? That's like first-class top-down context setting Okay, you do worse than emulate Abraham Lincoln a Second a different kind of plan so you can just kind of reverse it right zoom out start with the little picture We're building this Screen because we need or this page because we need a shopping cart because we are building an e-commerce site Because we want to get filthy rich Right. It's very simple So go to the other way Another kind of explanation is a process explanation Right. How does something work step by step by step? Right. How does rails handle a request? Well, it comes in it gets routed to the right controller The controller consults the model sends it on to the view the view formats the data sends it back out That's a process explanation process explanations are good plans for processes and Depending on your age at how much TV you watch there's a kid You'll recognize this process explanation or not. This is this was schoolhouse rock It was trying to explain how a bill becomes a law in the US And there was a little character. He's sitting there named Bill and he would go through the motions of you know Congress passes it and the president signs it kind of thing So process explanation There's also and again, none of this is rocket science, but it's something to think about there's the simple to complex So if you're trying to explain this bit of code to somebody, what do you say about it? Well, it depends on who the somebody is You would say one thing to an experienced Ruby developer. You'd say something different To an absolute beginner To an absolute beginner. Do you know what I say and I've said this many times. What is that? It's a loop That's how we do loops in Ruby Well, maybe Actually, it's a call to the each method Which takes a block which is actually a closure which captures the values of that That is not what you say to a beginner what you say to a beginner is it's a loop You say it's a loop and then you know you're gonna come back once they've written their first few Ruby programs and maybe have a clue about blocks and things you come back and you say Oh, well, let's talk about those loops and why they look funny Don't try to explain everything all at the same time because you'll end up explaining nothing forever Right, so you can summarize this strategy For explaining with one simple word you lie Right, you lie for good cause, but you lie now in particular You'll get in trouble with these kind of little white lies Not from the beginners who will love you and kiss you on the mouth for making it simple so they can get off The ground You will get in trouble from the experts somebody who really knows it will come by say back That's not a loop. That's a call to the each method passing in a block So I got an additional bit of advice for when you come across those situations right Explaining is so important That you lie cheat steal you do anything to get it across and if you're if you offend Some of the some people who don't have a clue about explaining that's okay They might be an expert in Ruby, but they probably don't know how to explain things Right, of course when you tell the lie make sure you go back and until the lie at some point So then it's not really a lie. So that's number one have a plan for your explanations number two is Be agile, what's it mean to be agile with an explanation? You have unit tests you drill in the people's heads You know the people you explain to and put little electrodes in there and see if they got it probably not That's kind of a what would be a slow running test anyway Being agile really if you get down to the core of what it means to be agile if you do it You measure it you fix it and your repeat. That's what being agile is So how do you measure The results of an explanation how do you know if your explanation is actually working right because to do it isn't hard Right stand up there and explain to fix it right we can figure out if it's not working. We can do something else We can certainly repeat it. It's the measuring part Well, I'm sorry that I have to say this but I've seen enough people inflict enough Failing explanations and not measure not see the signs that it's failing So let me give you three signs that your explanation is failing They look at you funny their silence or Even more key they start asking the same questions over and over and over. I don't I don't get this Well, what about this? I'm just not sure about this Okay, that's a flag that they're not getting this and that you should do something different Where something different is not just do exactly the same thing over and over again But the key thing is that when your explanations start to fail You need to keep something in mind It's you not them. I Worked for a company called relevance as I said and we have this thing Right. We don't just want to be good at stuff. We don't want to be great at stuff We want to be awesome at stuff and so we're always asking ourselves. Yeah, we're kind of full of ourselves We're always asking ourselves. What would be awesome here? So what's awesome in an explanation? Awesome in an explanation is not take this person who's sort of familiar with rails or whatever and get them up to the next level That's good. That's not bad. It's just not awesome Awesome is also not take this person who's sort of familiar with whatever it is and get them up to the next level Really really quickly. That's not awesome. That's that's better. It's not awesome awesome in an explanation is the take someone who has no clue and give them a clue it is to take someone who doesn't have the context and get them going and The good news is that there's a single failure mode That most explanations suffer so that when you start to get those blank looks and the same question Over and over and over you can think that I've probably got a gap in my explanation Okay, so what's a gap in an explanation? It's it has to do with the way we learn things If you're trying to learn Spanish, right? When you first are learning Spanish any really anything, but I'll take Spanish as an example When you're trying to learn Spanish and you need the Spanish word for red Initially you go through this painful conscious lookup process. What's the word for red the Spanish word for red is?  It's horrible. Everything is a fight and then you get good at it You've just forgotten that there's anything to know and that's great for learning things It's terrible for explaining things because experts know it so well They forget that there's anything to know and I think we were talking about this yesterday Somebody said actually set this up on the stage that there's you know a string is not what you people think it is right? That's an example of this right So that's the gap A gap in your explanation comes when you don't realize that you know something and you skip right over it And it just leaves this chasm in your explanation Right, and I give you a personal example of that about six months ago me and a friend of mine a guy named Dave Bach Did something very akin to what we were talking about yesterday? We kind of said if you want to learn Ruby on Rails come see us every Tuesday night We'll take about 30 people and we will do our darn this to try and help you learn it And we got a whole bunch of people some with a lot of programming experience some with almost no programming experience none of them knew anything about Ruby none of them knew anything about Rails and We tried to teach them so I want you to put yourself in my shoes If you had somebody who doesn't know anything about Ruby or Rails What's the first thing you teach them? What do you say that first day that first evening the first hour the first ten minutes? Talk about model view controller tell them how to install Ruby bundler RVM I don't know controllers active record right million things you could start with I think we started with like installing Ruby or Rails or something And there were three or four people and they all happened to be clustered in the back of the room and they just were not getting it I mean it was the same questions over and over in the blank stairs and the sort of confused dog on an angle head Kind of look and I knew it wasn't working and I kept trying different things and it just wasn't working and Finally, I almost saw like I saw like the imaginary light bulb go on and over this woman's head And she said oh, I mean it was like she had jumped the gap. She had figured it out And I'm like great. What is this gonna be and she said oh? Ruby is the language Rails is the framework Well, duh But you know what? Nobody in this room was born with that information coded into their DNA Somebody explain that To every single one of us and here's the good news Once you find one of these gaps Ruby is the language Rails is the framework hold on to it That's gold. That's the thing that no one else is explaining That's the thing that you can explain that no one else is explaining because it's disappeared from sight of All the people who know this Okay, and furthermore you can explain it to the explainers make sure when you teach them mention this And rails is the framework Okay, so that's number two mind the gaps Okay, number three Takes me in the sports Which is not a place I want to go I'm not a sports involved person My wife made me watch an hour of the Olympics this summer And I enjoyed all but like the last 55 minutes of it But I have a theoretical knowledge of sports and One of the things I know is that there's two different kinds of sporting games there's one kind which is baseball and Tennis and golf and maybe a few others and then there's the football kind Which includes hockey and basketball and soccer and a few others Baseball you play it till it's done right nine innings Right, if it takes two hours great takes four hours great It takes as long as it takes but you go through all the steps and then you're done Football there's clock 60 minutes 59 minutes basketballs like that hockey's like that so the question is What kind of sport is explaining We tend to treat it like it's baseball All right, I've got this subject to explain. I don't know Ruby on rails So I'm gonna start in the inning one. I'm gonna start with oh Maybe the stateless nature of the HTTP protocol and then I'm gonna move on the basic object-oriented Programming and inning two inning three is gonna be all about Routing and pattern matching because routing doesn't let a pattern matching Inning for maybe I'll talk about models inning five and maybe somewhere around inning seven We'll write our first Ruby application or rails application, right? You could see somebody doing that In fact, it's not gonna work because someone we're around inning two Everyone's falling asleep Okay, nobody cares anymore right explaining is a timed event There is a clock the clock runs When the clock is done, you are done explaining.  Where's the clock? It's in the head of the person who you're explaining things to Right, all of us have a limit on how much information we can take in Every single one of us, right? It's different on different days. It's different for different people. I suspect Having gone through a two-day conference your limit right now is a little lower than it was when you started, right? You just get overwhelmed Right, so what does it mean? Like what can we glean from the fact that there's a clock running in an explanation? How about this put the important stuff first? Right if you want them to know something stick it in the front then did this yesterday Right then said if he started this talk by saying if there's one thing you want to remember from this talk, it's I can't remember But and he put it in the front Another key thing Another key thing is that terminology is not the important stuff Okay, terminology when you're explaining something especially to a beginner is not the key thing Terminology is important Okay, terminology is the is the tool It's like a scalpel that an expert will use to separate the merely plausible from the actually correct Okay, but to a beginner. It's just an impediment Okay, especially given that if you put the terminology first, that's all they might get Here's an example. So you ever go to the eye doctor and they say better or worse better or worse, right? So we're gonna do a better or worse. All right got about 20 seconds And you need to explain computer Security a couple of the concepts in computer security Authentication and authorization even better. They both sound the light. That's always good Right. So here we go. Here's better or worse alternative one in computer security There's these two related with distinct concepts called authentication and authorization What have you really done? Absolutely nothing. There's a couple of a words or something, right?  Who is the person and what are they allowed to do? Which one would you rather have your office mate walk away with? One's important one's just terminology explain the terminology do it later do it in another session Do it at the beginning of conference The other good news about the clock is that it's variable Sometimes it runs faster. Sometimes it runs slower. Sometimes you can actually reset it give yourself 20 or 30 seconds more five minutes more How do you do that? Well, here's how you make the clock run faster Here's how you you run out of time and make sure you don't get to explain anything before the clock hits zero Tell them that this is really hard Okay, this next one.  Maybe push it back you get people small victories, right? You got something hard tell them after the whole thing about the plans with the With the explanations, that's really the hardest thing. I'm gonna tell you today Right, that's what you do. You don't tell them. This is gonna be hard.  Also, you can break it up if you can break things up into manageable chunks That really helps. I like the five ways to do something kind of thing. You may notice Okay, so that's watching the clock So next one number four Your bunch of engineers, what's that mean? Don't repeat yourself We love don't repeat yourself even back in my mechanical engineering days We were smart enough to know we don't put extra stuff in the machines They'll just break it'll get in the way it costs more to all the same when you're building a mechanism You don't want to have extraneous stuff. So don't repeat yourself So that's what dry means, but you know what if you look up dry in the dictionary It means some other things Having no adornment It was a dry movie just the story Impersonal he just gave us the dry facts God that Russellson does the driest talks and most damning of all Without butter Here's the thing Dry is for machines. Don't repeat yourself is for machines. It's for mechanisms. It's for things you build that have to work Make come as a surprise, but we are not machines People thrive on redundancy right Read any literature and it's full of references back and forth and people saying the same thing There's over and over that's called character development People are not machines. So you don't want it You don't have an explanation where you explain something For a long time and then just go right back and repeat it all over again But you do want to explain something and then come back to it and say do you remember when we talked about this? That's still important. So you want to repeat yourself enough and so I actually have a different acronym for that You find anything on the internet you really can that's Russell's reserve rye So So why do you want to repeat yourself you want to repeat yourself for emphasis? Let me say that again. You want to repeat yourself But mostly you want to repeat yourself for context Right, you want to remind people of where what I'm talking about now fits in with what I've talked about before So you don't want to like repeat huge sections of your explanation But you don't want to do something like the IRS always does right if you're a fill out government forms Right, they'll say something very helpful like refer to section 9.7 What does it say in section? What's 9.7 about because keep in mind 9.7 might be really really important So now we come to number five Which is probably the most important thing I'm going to tell you today and yes that does break the rule They put the most important thing first. Why am I doing that because I'm such an awesome explainer I know I can carry you all along so the most the Most important thing has to do with this book and I actually a copy of it right here It's called numerical methods that work You see when I was in college here is like a sophomore in college I fell in love with this mathematical technique called numerical analysis, which is what this book is about and I got a whole bunch of books out of the library and instead of doing what I was supposed to be doing I spent like the whole semester reading about numerical analysis and writing programs and The details of an American analysis aren't really important The thing to keep in mind is that it's a mathematical technique that sometimes works brilliantly and very occasionally blows up horribly just awful yet answers that aren't even close and So I had all these books spread out on the library table And I was next to a window and the Sun was streaming in and this book Well, I bought this one on eBay and steal from the library This book was sort of sitting there like that the Sun was hitting it And I realized that there was like something else on the cover that looked like letters You couldn't quite read it, but and it's sort of you know, I spent the next half hour What is that and eventually I did that thing that people do with monuments sometimes you get the piece of paper You put it down there and you get the pencil right and you spread all over it and I did that a few months ago and Well, there's where the thing was I did that a few months ago I don't know if you can read it Here's the thing It's one small joke.  It's nowhere else in the book You know it with the title nowhere else is there a hint that that usually is there Right. It's one small joke and here's the thing. I Can't remember the title of any of the books I read that semester Except that one. I had absolutely no trouble Finding that book on eBay a few months ago It's one small joke that made me remember something for decades So number five is mixing some humor Okay Which brings up the question. Are you funny?  I think of myself as sort of funny. I can be funny sometimes, right? So don't let the jokes get in the way Subtle is better, right that that word is just kind of embossed. They're waiting for somebody to find it and For God's sake, don't explain the jokes jokes are not a place to explain anything Okay But now we come to the hard case What if you're not funny and you know it, you know, you're not funny Congratulations your head and shoulders above the people who aren't funny and don't know it, right? So that's that's good Okay It doesn't really matter if you're funny or not humor is one way to get to what I'm talking about But it's not the only way Well, I said mix in some humor. I really mean mix in some humanity Okay, you need to show up at your explanations. You need to be there You need to let the person you're explaining things to know why it's important Right I Brought my book. That's the little piece of me that I brought But if you think about this conference with all of the incredible speakers we've had right Sandy brought the baby Which is possibly the only time that those words will ever be uttered What more can I say? Then brought God well the God class right then was willing to say here's some code that I'm not exactly proud of Let me show it to you that takes some stuff Right Angela brought a cold Right, but she also brought Her heart, right? Anybody not feel that anybody not pay attention Right you need to show up at your explanations You need to show up because explaining is one of the most important things you are gonna do Right you write some code and then you explain it for the rest of your life Okay, you need to show up at your explanation. I can tell you all the stuff, right? I could say that people are social animals and That by showing up at your explanation you pop provide an important social context Or I could tell you that it just makes the explanation more fun more interesting But really it just comes down to Seven simple words if you don't care.  I wish you safe trip They also wish that when you get back to your office You think about what all of these techniques, but most of all you think you start explaining you start explaining because It will make your company better. It'll make your work environment better It'll make the people around you better it might even make the world better And I think you're just a group of people to do it. Thank you all for listening Sure be happy to do questions if anybody has any sir Do it over and over and over I'm sorry. The question was how do you well? It's hard for me to repeat the question How do you how does he get as good as me in presenting and really it's just all about practice.  Maybe it's not so disastrous. That's that's the difference So anyone else? sir, I Think you have to treat it as like an interactive kind of thing. I think you need to Let people know when you're completely lost like you need to give them some rope like they might lose you But they might get you again But at some point if you're completely gone It was like I forget who was talking about the the bad pair programming kinds of things you need to You know pull on the rope the other thing you can do is so frequently the most common failure mode with an explanation is this gap they've skipped over something that's not there and You can help people explain things by saying, you know what pretend I'm a third grader now explain it to me Right now. I don't get that pretend that's a fifth grade explanation pretend I'm a third grader, you know and pull them in and eventually They'll say it maybe They want us all right. Thank you all again


In this video, we're going to talk about how to graph the function h of x equals the square root of 1 minus x plus 2. We're also going to talk about the domain and range of this function. So the important thing to remember here is that this is going to be based upon, well, the basic graph here. We have to identify what's the basic graph without any of the transformations going on here. Like if I give rid of this 1 and the minus sign, I give rid of the plus 2, the basic graph in play here is going to be the square root of x. And so that's kind of like step zero when it comes to graphing these things. We want to look at the basic graph y equals the square root of x. And then we start identifying transformations we've done to that. And the square root of x is going to look like this graph right here. It goes to the right, something like that. And so then what do we do? Well, we can very quickly see things like the negative in front of the x is going to tell us that there's a reflection of some kind. A coefficient of negative 1 tells us there's a reflection. A negative one in front of the x is going to be a horizontal reflection, aka a reflection across the y-axis. If you saw a negative sign in front of the square root, which was the basic function, that would be a vertical reflection across the x-axis. We don't have such a thing here. So we're going to be reflecting across the y-axis. So our standard graph is going to reflect over, let me clear it out now, it's going to be reflected across the y-axis. And so it's going to then appear this way. So it's the same square root, but now it points to the left instead of points to the right. Then we want to shift things vertically by 2, right? If you look at this plus 2 that's outside of the square root, the plus 2 we're adding to the function f of x here. And so this is going to move the entire graph up by 2 units. And so if we then take a look at that picture, our square root now has been shifted up by 2, and it would look something like that. The final step here is to figure out what does this plus 1 do right here? The plus 1 is actually going to be a shift to the right by a factor of 1, which you can see here, our final graph. We could shift it to the right by 1. It should go 1 to the right. But why to the right? Why isn't it a shift to the left? Isn't it a plus 1? Well, this is the issue we have to worry about, right? When we talked about the order of operations, we always did reflection first, then shift, then scaling, then shifting, right? And an important thing you have to have here is, if ever, this is, again, the weird consequence of the horizontal zone. If ever the coefficient of x is anything other than 1, you should factor, you should factor the coefficient of the x. Otherwise, you might be getting the wrong transformations here. So the fact that we have this negative sign in front, what I want you to do is factor it out. So rewrite the function as the square root of negative x minus 1 here. Let me write that. So we factor the negative 1 from the x, but we have to also subtract away from the positive 1, like so. So we really want to think of this as the function square root of negative x minus 1 plus 2. And you'll see here that when you look at this factored form, you'll still see a negative sign. So that means reflect across the y-axis, because you have a negative in front of the x. You'll still see this plus 2 outside of the square, which will still mean shifting up by 1, shifting up by 2, excuse me. No difference there. But now when you look inside of the horizontal zone, you see a negative 1. And this correctly indicates to us that we want to shift things to the right. And so the order of operations matters here. This function, the original form, actually was doing a shift then a reflection, but we agreed earlier that we're going to reflect and then we're going to shift. So to avoid those confusions, always factor the coefficient away from the x. And if you're adding something to the x, that you'll need to factor away from that as well. So you prefer to see the horizontal zone factor. The horizontal zone should be factored. Let me even write this on the screen. The horizontal zone should be factored. If it's not factored, you're going to probably get a lot of headache there. Life will be easier if you factor the horizontal zone. So we've correctly identified the transformations in play here. What does this have to do with the domain, right? One thing we could see here is that this is a square root function. The horizontal zone is going to affect the domain of this thing, right? We could then look like one minus x is greater or equal to zero. We then solve and get one should be greater or equal to x or x is less or equal to one. So notice you can very quickly identify that the domain of our function h here is going to be all numbers less than one. And you can see that right here, right? You have one and then you get everything to the left, but you don't get anything to the right. That's the correct domain. We can solve that algebraically, but I should also mention that we can find the domain of this thing perfectly geometrically because if we think of the original graph, y equals the square root of x here, y equals the square root of x, its original domain is going to be all non-negative numbers, zero to infinity. And so if we pay attention to the transformations we did, reflected across the y-axis, that changes the domain to be negative infinity to zero because now the graph, instead of being on the left-hand side, the right-hand side of the y-axis, it got shifted over, reflected over to the other side. So you switch the domain when you did that horizontal transformation. In terms of vertical transformations, you shift it up, that didn't change the domain. Then when you shifted everything to the right by one, you move everything over by one, what that does is you didn't get a picture over here, that's going to shift the domain one more time, giving us the current picture we see right there. And so every time you do a horizontal, oops, I got way much backspace too much here, every time you do any type of horizontal transformation, it changes the domain. And so with this one reflecting across the x-axis, you do standard graph, remember, the domain switched from zero to infinity, that's the standard one. This horizontal transformation switched the domain to be negative infinity to zero, and then shifting it right switched the domain to be negative infinity to one, which is the final domain. So by changing the graph with horizontal transformations, you change the domain because isn't the domain, the set of all possible x-coordinates, which the x-coordinate is the horizontal component, the horizontal coordinate for the graph. So every time you change the horizontal, you change the possibilities for the horizontal, which is what the domain is. Could we do the same thing for range, right? Because we have algebraic ways of finding the domain, we don't need to do this idea of transformations, but we're not very good at finding the range of functions yet. What if we did the same game for the range? Because the standard function, the square root of x right here, it could go up and up and up and up and up, it goes off towards infinity there. So its range, the range here, is likewise going to be zero to infinity. So that's the default range for this basic graph, zero to infinity. Well, what happens if we shift everything up by two? Well, if we shift everything up by two, we go up, we get a picture like this, and then the horizontal transformations come into play. If you shift everything up by two, the range would then change to be, it's not going to be this anymore, it's going to be two to infinity, right? The range goes up when you shift it up by two, and so the range would then go from zero to infinity to two to infinity. So if we know the domain and range of the original function, the original graph, and then if we apply the appropriate transformations, horizontal transformations affect the domain and vertical transformations affect the range, we can then actually determine without any algebra whatsoever the domain and range of the final function. And I mean, there is a little bit of hiccup there. You have to know the domain and range of the original graph, but knowing that we can find the domain of the range purely geometrically by identifying the transformations. And this actually gives us a very powerful way of finding the range of a function for which at the moment we don't have really a good algebraic way of finding the range. The range is in this situation best studied by looking at the geometry. And so that's going to bring us to the end of lecture five here where we've talked about graph transformations. Graph transformations are deeply connected with function composition, right? This function right here, we could decompose it. Each of these steps we do is a decomposition here. We see that there's this plus two on the left-hand side. There's these negative and negative one. Decomposing the function is actually identifying graph transformations. And we can see in this example that even if we're only interested in the function algebraically, the graph transformations help us understand better the domain and range of the function based upon these transformations. If you feel like you learned something in these videos, please hit the like button. If you want to learn more, feel free to subscribe to learn more about new math videos created in the future. If you have any questions as you're watching any of these videos, please put your questions in the comments below. I'd be happy to answer any questions you have. And until next time, keep on computing. Keep on doing some good mathematics. And hopefully we'll learn some more college algebra in the next video. Bye, everyone.


It has been 100 days since Keir Starmer became Labour leader. Paul's show, he's made a good impression on much of the public. He's seen as competent and credible. But what does he actually stand for on no subject? Is this question more mysterious than on tax? And in particular, the issue of a wealth tax has, this has got Labour tied up in knots about what it actually believes. We're hearing one thing one day, another thing, another. So this issue, this particular issue about wealth taxes, first reared its head when Annalise Dodds the Shadow Chancellor in a speech on the 3rd of July answered a question about wealth taxes like this. When it comes to wealth taxation, I mean, again, we have seen many changes in this area over the years and we've seen actually an increase in inequalities in wealth over the years. I think the government does need to look at this area. I don't think we're in a fair situation where the amount of tax paid by the very worst off people is actually less proportionately as part of their income than that for the very best off. And of course, for the very, very best off people, quite a bit of their money coming in is derived from wealth. I think we do need to have that new settlement. And actually much of the opinion data has indicated that that's got a lot of support amongst the UK population as well. That position was echoed on Ma the following Sunday. As she told him, we have seen a rise in income and wealth inequality and those with the broadest shoulders should be bearing more of a contribution if that contribution is needed. And then the following day, Keir Starmer confirmed to Nick Ferrari on LBC that Labour supported the principle of a wealth tax. We can take a look at that moment here. What's up? Your Shadow Chancellor has spoken of a potential wealth tax. Is that the solution to this financial crisis? Well, she said, look, it's got to be amongst the issues that we look at. She's right about that. So you would support it? Well, we are saying to the government, look at the idea of a wealth tax. We certainly support the principle that those with the broadest shoulders should bear the greatest burden. But at this stage, four years before an election, I'm not going to start setting out tax. But where would it kick in? Well, we'll have to look at it carefully and we will have a fully-costed Labour manifesto in due course and a much shorter one, by the way, next time. So that was a decent line. He's saying, in principle, we back it. We think that the cost of the crisis should be borne by the wealthiest, but he wouldn't be drawn on detail totally fair enough. I think the last leadership often got to bog down in detail too quickly. However, two days later, after Sunak's mini-budget, Dodds took a different tone. She stated, then, Labour is not calling for tax rises. We are calling for growth. So we've got Labour is not calling for tax rises. A much more definite statement and against wealth taxes. That generated this headline in The Times. Can we get this up? Labour backtracks from wealth tax plan. That article was, in turn, confusingly pushed back against by Dan Cardin. So he's a shadow treasury minister, one of the few left-wingers remaining on the front bench of The Times article. He said, this is false. Labour is clear that the cost of the crisis should be borne by those with the broader shoulders. We are following very closely the academic research underway by LSE inequalities and Warwick University and others on how a UK wealth tax would work. But Cardin, one of the few left-wingers remaining on the shadow front bench, was put back in his box on Sunday when Andrew Ma asked Rachel Reeves the following. But before long as a country, we are going to have to pay for all of this. If Rishi Sunak came to the Labour Party now and said, look, I'm afraid that everybody earning over, say, £80,000 a year has to pay more tax to get the public finances back in support, would you say, no, we're against those tax rises? Well, we would look at any proposals that the government have put forward. And under Keir Starmer's leadership and with Annalisa Dodds as our shadow chancellor, we have tried to be a constructive opposition to support the government when they get things right, but to push them further, including on jobs and support with the flexible furlough scheme that people want to see when we think the government needs to do more. But right now, we think the entire focus of government and the Treasury should be to get people back into work. Sorry to jump in again, but asking people earning over £80,000 a year to pay more tax was a Labour policy. Have you really moved away from those kind of policies? Labour is no longer the party of fair taxes, of taxing people with the broader shoulders most. Is that really the position? Well, we're not setting out proposals at the moment for the next manifesto. The next general election is likely to be four years away. We had a terrible defeat in the election last year. We need to reassess a whole range of policies, and I'm not going to write our manifesto on an ad hoc basis on this programme, Andrew. There's plenty of time to do that work, but right now the focus has got to be on jobs. Sometimes when you see Labour front-benches at this point in time, and yes, they're doing quite well in terms of public popularity, we'll go on to that, but it does sound like you've pulled a string behind them and they say the same sentence, whatever the question. So she's asked, do you support the principle of wealth tax? We decided we're going to be a constructive opposition, so whatever the government wants to do, we'll look at the details and then we'll decide. But what do you think about a wealth tax? We want to be a constructive opposition, so we won't have a manifesto for another five years, so until then we'll just be constructive, we'll listen to what they say, we'll look at the details and then we'll decide. And this whole idea that we're not going to write our manifesto till 2024 is complete nonsense. Yes, he's not asking you, and he shouldn't ask you the details at what threshold is someone going to have to start paying this new tax and is there going to be, you know, are you going to ramp up HMRC so that they get all of the detailed questions? Yes, put that in the manifesto. But do you support a wealth tax? That's an issue that matters now. Before 2024, many of the decisions that get made, over the next year or two, are going to be incredibly important in setting in, you know, a new economic settlement in this country. And do you want to have any role in that? Do you want to say, do you want to be pushing the conservatives in a progressive direction? Or do you want to just stand back and refuse to have an opinion on absolutely anything?  Ash, Keir Starmer is proving quite popular, the polls are showing, but you know, I suppose seeing constructive opposition seem quite as shallow as that can be rather frustrating. Well, I've written on Keir Starmer's constructive opposition approach quite extensively, and I've tried to be really fair to him because I know Keir Starmer's politics are not my politics, and it would be unfair for me to criticise him on the basis of simply not being Jeremy Corbyn, of simply not being John MacDonald. Address Keir Starmer for who he is.  That's what he wants to do. And the way in which he wants to do that is, on the one hand, is bolstering his perceived strength on the areas where Corbyn was perceived to be weak, so internal party management, and reintroducing a aura of professionalism to the Labour Party project, law and order, and foreign policy. Those are the main areas. But what I think he's leaving out, and I'm fine with him doing the whole, I'm a sir, I've met the Queen, I'm a QC thing, fine. Whatever Keith and Harrogate needs to hear, fine by me. What concerns me is there's a complete unwillingness to change the conversation in a direction which might be more beneficial to his political party. Because at the moment, Labour policy on tax is being outflanked on the left by actual millionaires. There's been this lesson of millionaires for humanity saying, please, tax us a bit more to be able to pay for this crisis. I think that it's likely that in certain policy areas, you will see Rishi Sunak in particular being more interventionist and advocating more interventionist policies than the present Labour front bench. And that's a dangerous place to be in. I reckon that should Leila Moran win the Lib Dem leadership, she's going to be pushing for visionary things like UBI, requisitioning private hospital capacity, perhaps even a four-day week. And you start seeing a fragmentation of what was once Labour's most reliable core vote, young people, working age, working class people, students and so forth. And these radicalised homeowners, they might like you. They might think that you're better than Corbyn before he is in when the honeymoon's over. Are they going to return to you and give you their vote? Simply because the totems of outraged Middlingland, Jeremy Clarkson, Piers Morgan have said that.  I think no. And I think that that's where not taking the chance of trying to persuade people of things like wealth taxes, of having a green new deal with a clear 2030s target, this is where you're really shooting yourself in the foot.  In the meantime, you've had, I think, a lot of your support become disenchanted.  And some of them might go green. Some of them might go Lib Dem. And a chunk of those radicalized homeowners are going to stay conservative.  I would say, shall I just invite you back in 2024 then? I mean, what's the point in you turning up for the next four years and refusing to have a concrete position on anything because you're not quite yet ready to write your manifesto? I mean, what are they going to do for the next four years? You mentioned the millionaires, the 83, I think it is multimillionaires who are backing more taxes. Obviously, I don't know how representative they are of millionaires in general, but the public. And we've got some concrete data on them. 61% of the public support a wealth tax for people with assets worth more than 750,000 pounds. That's excluding pensions and main homes. We've only 14% opposed. There are other polls showing that, actually, it's the majority of conservatives who support these kind of policies. And potentially even the Tory party now could come out in favour of hikes on taxes for the rich before the Labour Party do. So Guido Forks tweeted out today that Tories, or Patrick McGuire from the Times, tweeted out from Guido, that Tories have asked members which kind of tax hikes they would find most acceptable. So it could be the case that the Tories come in first here and then Labour have to constructively accept these tax rises unless they want to try and outflag them from the right. I don't know. Aaron, what is going on here? Wealth taxes are popular with the public. Let's put this in a different way. We know that Keir Starmer wants to be popular with the public. He thinks that the previous administration took on too many battles, took too many positions that people that he wants to appeal to weren't onside with. A wealth tax wasn't one of them. This seems popular across demographics in this country. Why is he not just coming out and saying, yes, of course, we support the principle of more taxes for the very wealthy so that we can rebuild a more equal society which coronavirus has shown is so desperately needed? Of course, he's not very good at politics.  His chief of staff, Morgan McSweeney, a lot of people say he's a really talented guy. I mean, I have no idea. Look, he's working for the Leader of the Labour Party. He's working for the Leader of the Opposition. So I presume there's obviously some truth to that. But you know, he was working for Liz Kendall in 2015. And so I do wonder, in terms of their instincts, I wonder how good they are. And of course, the coronavirus has created a political environment now, which is heavily dependent on instincts. And I really don't think Keir Starman knows what he thinks in this context. And I think what Ash said about the Lib Dems, I think there's a very real possibility that if Leyla Moran does become their leader, and right now she's not the favourite, right now, Davey is the favourite. But if Leyla Moran was to win that, I think Labour would lose seats in the next general election. And that sounds like a huge claim. But you know, people talk about the Red Wall, which is another blue wall. In many of these seats, which the Labour Party just held on to by 1,000, 2,000 votes, if you lose a couple of hundred young people, a couple of hundred Bane people, if the Tory vote basically stays where it is, those seats are gone. In Laboury seats, only a 700, 800 majority. And I do think this is something that the Labour Party needs to be alive to. You know, in 2010, they got 28.5% of the vote. Why? Because Nick Clegg did so well on a message, and it was just a message, there was nothing to it, of being more progressive than they were. In 2015, they got hammered fundamentally because they lost votes to yes, the Tories, to UKIP, yes, the SMP, also to the Greens. You know, the Greens got almost, I think almost a million votes in 2015. You know, there were like 15, 16 seats. It basically would have been a hung Parliament if a lot of these Green voters had all voted Labour in sort of Lib Dem, Labour or Labour Tory marginal seats. And of course, that wasn't going to happen, but it's an interesting thought experiment. And I can see a repeat of that in five years' time. And, you know, it's kind of like, we're stuck in this time warp, Layla Moran will promise the scrap tuition fees, and then she'll enter some coalition with the Tories. Presumably not, maybe even in that scenario, Labour will say, well, we could have some kind of, I can almost see it now, you know, Jeremy Gilbert and Clive Lewis and Paul Mason, all these people are like saying, we're going to have a progressive alliance between these two parties, and the Lib Dems are talking about a four-day week and a UBI. I mean, maybe, right? But that's not what the critique of Corbynism was about. The critique of Corbynism was, you know, Jeremy Corbyn's taking us to disaster. And I do feel that there's a very raw possibility that Labour get fewer seats next time around if Layla Moran wins. It's a big, big problem for Kirstam. It's a really big issue. You know what? I think it probably will be ignored because the fundamental worldview of the people around him is that you don't need to appeal to progressive voters. You don't need to do that. You just need to appeal to a small 15% part of the population, you know, home-owning men in marginals. That's not going to be good enough in a context of the S... That used to be the case when it was a two-party system with the SMP, with potentially the Brexit party. You know, this has not gone away, and they need to have a much more nuanced approach to this. I mean, there's also potentially a more conspiratorial explanation for all this, which it isn't just about appealing to that 15% of the electorate that live in swing seats, but it's about appealing to the one or two or three or four people that control Britain's press. So wealth taxes are very popular with the wider public, popular with Labour members, the people they're not popular with, the likes of Rupert Murdoch. And if Kirstam is still thinking it's a possibility that he can get the Times, the Sunday Times, Talk Radio, The Sun, all of these organisations on side, many of them backed Tony Blair in 1997, he can't be supporting things like wealth tax.  He's also disagreeing with himself. Let's get up. The first pledge of Kirstam was famous, 10 pledges, which helped him win the Labour leadership. It was, increase income tax for the top 5% of earners, reverse the Tory cuts, incorporation tax, and clamp down on tax avoidance, particularly of large corporations. No stepping back from our core principles. No ambiguities there are there. All the ambiguities, shock horror, were introduced after he'd got the votes of Labour members.


The next item of business today is the member's business debate on motion number 13952, in the name of James Dornan, on step change debt charities action plan on problem debt. This debate will be concluded without any questions being put, and I would ask those members who wish to speak in the debate to please press the request to speak buttons now. I would also ask guests leaving the gallery to note that this Parliament is still in session and please do so quietly. I want to start off by thanking those colleagues who signed the motion and those who are speaking in this important debate on personal debt problems. I would also like to pay tribute to step change debt charity for its hugely successful work in the area of personal debt crisis and for its assistance in preparing for this debate. I am sure that other members have been beneficiaries of the excellent research provided by the charities' public affairs officer, Mr James Stewart and Gillian Thomson, a trustee who are present in the gallery today. I want to thank all his colleagues for the help that they have given us. Step change is the largest provider of free independent debt advice and managed debt solutions in the United Kingdom. Last year they helped 16,000 people, a figure that has almost doubled since 2012. They boast an impressive stat that 97 per cent of their clients who enter statutory debt repayment solutions successfully pay off their debt. That is the highest of all debt providers in Scotland. That is a commendable feat and one that has helped to alleviate untold stress on many families and individuals in all our constituencies. That is achieved by providing their clients with a tailored and detailed financial plan that reassures both the client and creditor with affordable repayments. That undoubtedly brings hope to those who once felt hopeless. In cash terms, debt change helped their clients to pay off £30 million of debt in Scotland last year. I recently visited their Scottish headquarters in Boddwell Street and was granted permission from the clients to sit in some telephone consultations. The conversations between clients and advisers raised a number of issues. The first was that, despite the Tory Government's assertion that indebtedness is an issue for, in their words, the unemployed and the effectless, step change's research demonstrates that this is clearly not the case. Around one-third of clients are in full-time employment and another 30 per cent are unemployed and the remaining 40 per cent are those who have retired or students, carers and those in part-time employment. The adviser I was attached to, Michelle Robertson, shared with me two calls that particularly stick in my mind. The first were two doctors, GPs, who had £36,000 of payday loan debts across 27 different individual loans. These clients are not low-wage earners, they are not unemployed or sick or in firm. They are a well-paid couple who still find themselves dragged into the debt trap. That highlights how anyone can be caught in a spiral of misery. The other call that I was told of was much more concerning. A gentleman had taken out a payday loan of £60 over a three-day period. After missing the first repayment date, interest in charges escalated and, by the time he contacted step change, his debt was £3,500. By the time step change was able to put a hold on it, it was £5,000. That is just wrong. It is morally wrong, economically wrong and, in my view, it should be legally wrong to charge such exorbitant levels of interest. Step change has conducted regarding the effects of the proposed Tory tax credit reforms, so that currently 17 per cent of step change's clients who have three or more children are running a budget deficit. If those horrendous reforms are carried through, that figure shall take an astonishing leap to 90 per cent, with an average loss of £231 per month. That clearly demonstrates beyond doubt the importance of tax credits and assisting families to simply make ends meet. Without playing political games, I do want to say that the sooner this Parliament has the power to create its own tax credit system, the better for everyone affected by it. What is also extremely worrying is that step changer is seeing the make-up-of-client's debt shift from credit card debt to arrears and essential bills. In 2008, the average debt of a step change client was £25,000. The good news is that this has fallen to £14,000. However, now that debt is comprised mainly of rent arrears, council tax arrears and utility bill debt, both in the socially-rented accommodation and the private rented sector. A accruing debt has now come from buying things that it would like but could do without, to having to fall into debt to stay in your home and keep your utilities on. While there is clearly still a huge debt problem in Scotland, it is widely recognised that the efforts of the Scottish Government have assisted in providing help to those with debts. Scotland is the only statutory debt arrangement scheme in the UK, and it is a six-week breathing space that freezes interest rates and charges to allow a manageable and sensible debt repayment schedule. That is not available to clients in any other part of the United Kingdom, and we should be proud that we are leading the way. I not only commend the sterling work that step change does but acknowledge the many successful outcomes that James and his colleagues have reached for their clients. Their action plan outlines how this Parliament can help to ensure that Scotland continues to help those with debt problems. I recommend all members in the chamber to read it. I urge all members to contact step change and see how they can help you in your constituencies. Their research is thorough and detailed to a constituency level, which is very helpful in getting a feel for the local situation. None of our constituencies are free from personal debt. Step change reaches out to all our communities and provides vital help, and for that, it should be strongly commended and supported. We now turn to the open debate speeches of four minutes. I call Ken Macintosh to be followed by Gavin Brown. I thank my colleague James Dornan for bringing forward today's debate. I think that a particularly timely moment for the debate is the run-up to Christmas. Many families should be looking forward with some sense of anticipation and excitement, but the gross materialism that is so typical of Christmas these days means that it is a time of anxiety and dread. Many families will simply be asking themselves, how do I get through this? How will I survive Christmas? Of course, we know the answer. They will turn to loans, debt and credit cards and everything else increasing this problem. I also thank step change not just for bringing forward the briefing and for the help for today's debate but for the work that it does in helping people across Scotland and across the UK. I had caused to refer three constituents in one family to step change just two weeks ago. This is a family—three working adults, I may add, and mother and two young adults in their 20s—all of them in work. All of them in work. The mother had a permanent job for some time, low-paid. The two sons were in and out of work. What had happened in the last couple of months is that one of the sons had two part-time jobs and he lost both of them. The other son lost his part-time job. The effect on the family was catastrophic. The difficulty of the family had been in and out of work for several years. They fell into council tax debt in 2010 and were in and out of council tax debt in the rears and other council debt for five years now, constantly being threatened with court action and reaching arrangement schemes. They were faced with court action this week. The council has tried to arrange a payment plan in the middle of rearranging a payment plan, but often what happens in such situations is that the payment plan is one that is unaffordable to them and so it is not manageable and it creates another crisis. Those are very difficult issues. There is no doubt about it, but it points to the sort of help that step-changer is highlighting here. Very small savings to give people the resilience to survive, plus financial advice and support to see them through. Difficult issues but step-changer are pointing the way through. I am not sure how typical this family is, but I do think that it is untypical. I was conscious of the fact that James Dornan said that those are not unemployed, not feckless irresponsible people. They are often families and I would also make the point that I do not want to replay the tax credits argument either, but we have the powers here to make a difference, so let us use those powers. It will help some of those people. There is also another group that is a generational issue. A lot of the people in the growing problem of debt are young. I think that two quarters of between 25 and 35-year-olds are anxious about the current debt compared to about a third for those over 65. I want to just, if I can just mention my constituency, because I have sent the statistics by step-change and it is quite worrying. Eastwood clients had the highest average debt in Scotland—23,500 per person—the highest in Scotland. Over a third were in the rears of the council tax, such as the constituents that I saw. 15 per cent of clients had a payday loan, with an average balance of just under £2,000. I noticed that that was growing every single year, increasing every year, and a quarter had renter years. You can only surmise as to why that might be the case. I imagine that it is linked to the fact that Eastwood is a relatively prosperous area. I believe that, with higher incomes, you can borrow more money, so you get into deeper debt. However, it shows that the problem is across the board. If I can very briefly turn to some of the things that we can do, financial education is vital. One in five people cannot even read a bank statement, so financial education is vital. Social advertising from the Government—I admit that it is difficult—we can spend thousands or perhaps tens of thousands, or, as longer, we are spending millions of tens of millions, but it is something that we can do. A breathing space that we have been talking about that the Government has introduced, I asked the minister, Mr Ewing, earlier this year, what his position was in extending the six-week breathing space—the moratorium on diligence—under the debt-arrangement scheme. At the time, he said that it currently can be extended in prescribed circumstances, but he had no plans to further extension it. I would ask him whether he is looking at this because it is clearly very helpful to lift that threat from people in their moment of crisis. However, the most important conclusion from step change and the most important recommendation is that £1,000 in savings would protect 50,000 households in Scotland from problem debt. There are so many things that we are doing currently that we could build on. I draw the minister's attention to the I Save Credit Union, Renfusure, the Savvy Savers in South Lanarkshire and the Future Savers scheme in Glasgow, all based on credit unions, supported by our councils that usually give pupils' nests £110 to start a scheme, and it gets them in good habits, hopefully for the rest of their life. That is the sort of initiative that could really make a difference. It is something that the Government could support, perhaps underwriting with a loan guarantee scheme. I would ask the Government to look at it. I would end by congratulating Mr Dornan yet again on bringing today's important debate. Many thanks. I now call Gavin Brown to be followed by Sandra White. Presiding Officer, thank you. I also start by congratulating James Dornan on securing this debate and on raising an important issue, and I think highlighting an excellent report that is conducted by step change. I would say at the outset though that if we are serious about doing something to help families across the country, our time is far better served, discussing the excellent report instead of making partisan and political remarks. I hope that the minister will focus his speech on the report and what we can do instead of making partisan remarks. The report covers a range of areas, but it also comes up with six excellent solutions, all of which require further investigation and two of which I want to focus on in the course of my remarks. Ken Macintosh is right to say that this time of year is a particular challenge for families. No time of year is easy, of course, but Christmas presents a particular challenge, which is a good reason for having the debate now. The problem, which is already widespread with 3 million people across the UK, could potentially grow as the years go by, with the challenges that we face in the global economy, Euro difficulties being delayed but not resolved. However, the biggest challenge of all, and one that I have to say I genuinely fear, is that at some point, whether that is next year, the year after or the year after, interest rates will go up. Interest rates can hardly come down, they have been at half a per cent, they have become effectively normalised at half a per cent, but when interest rates go up, whether that is to 1 per cent or 2 per cent, that will cause a whole new generation of problems for tens of thousands of families across the country. So now is the time to put in the hard yards the big effort in a cross-party, cross-national basis to try and make sure that we get on the right path as soon as we possibly can. Presiding Officer, the two issues in particular, which I think the issue raised that I want to focus on are this. One of the solutions from step change, focused on pages primarily 10 and 11 of the report, is calling for a review of affordable credit, trying to seek far better alternatives to the high interest credit that those on low incomes generally face. We read in a previous step change report that 29 per cent of total debt is on credit cards, which have some of the highest APRs and rates. This will not be an easy challenge to review, because typically the more money somebody has, the better prospect they will get, the lower credit terms they will get, the less money they have and particularly those who need it most will get the highest and most challenging credit terms. It is not easy, but I have to say that I was particularly impressed by the good shepherd project in Australia, which the report highlights. A microfinance programme, which pools a range of charitable government and financial services support and funding, provides different low-income loans and grants to suit different circumstances and provides available mainstream banks and high-street outlets locally. It appears to have been a big success in Australia. I know little about it other than what is in the report, but it strikes me as perhaps a very good starting point to try and help people not just in Scotland but across the UK as a whole. The second point, which I think was particularly strong in the report, is the idea that we need a pretty big expansion of free debt advice. There are very good charities out there. Step change do a particularly good job. There are government schemes too, Presiding Officer, but with 3 million people across the UK being in serious debt problems at the moment, we need to do much more. The people that we are currently reaching are those who are best placed to sort their problems out. The ones that I worry about most are the ones that do not come to debt charities, the ones that literally put their heads in their hands and allow their stress to grow. With every week or month that passes in that situation, it becomes more difficult to resolve the problems and the debts rack up in a sometimes frightening way in the way that James Dorran talked about in his second example. Presiding Officer, getting debt advice in a more innovative way so that we start to reach the people that currently, quite simply, are not being reached seems to be something that we need to look at pretty urgently. I would ask the minister to address both of those points so that he has time in his closing remarks. I also thank James Dorran for bringing this issue to the chamber today. There is no doubt by the evidence that we have seen in the papers that have been given and also by the contributions from other MSPs that people are increasingly finding it difficult to manage. As Ken Macintosh had said with the Christmas period coming up, he had these huge advertising campaigns aimed at parents for children. It is obvious that people get into debt and find it very difficult to get back out of it again. I congratulate Step Change and the other organisations that provide help and advice during a very difficult period for many, many people. Like James Dorran and I have visited Step Change, it is in my constituency in the Glasgow city centre. I am very impressed by how it is handled there. The first thing that I did twice is that I spoke to the staff, because I am always conscious of the fact that, in some cases, it is based on how many calls you take and how quickly you alleviate the calls that come in. What impressed me was the fact that people took their time over those calls. I was also allowed to listen in and to the clients' heads, to some of the issues that were raised there.  They phoned them while they were out with their mobile phone to give them advice as quickly as possible so that they could go down and sort something out. I was very impressed by what was offered through Step Change and the debt change. I really hope that they continue to provide that advice. Like Ken Macintosh, many people believe that my constituency in Glasgow-Kelvin is a very affluent constituency. It is in certain parts, but we also have problems. I want to give you a couple of figures that will probably surprise people when they think of the Glasgow-Kelvin constituency. In Kelvin, more than one third of my constituencies were in rears with a rent. 17 per cent had electricity and built rears. 41 per cent of clients had council tax rears, and 16 per cent had a payday loan with an average balance of £1,560. As Ken Macintosh said, if you get more money, you can afford to take out more credit cards, etc. The importance of not just this debate but the fact that we have these organisations is that it is important for this Parliament and for us to ensure that people know that these organisations exist. I think that that is a big problem, and I come on to the issue that Ken Macintosh raised. People hide their head in the sand, unfortunately, but if they were more aware that there was help out there—I think that is our job and others, the Government's job as well—to ensure that the people know that it is out there, they may contact them more timidly, and that is where the breathing space comes in. We know that we in Scotland are very lucky, and James Dornan and Ken Macintosh have also mentioned that. We have that advantage over other parts of the UK that we have in this breathing space, but it has already been mentioned that it is only six weeks. Sometimes, when people take that big step to contact organisations, they are already three or four weeks in arrears, and by the time they fall with their papers and contact various people, the interests in those debts are mounting up. I would like to ask the minister any summing up. Is there any other way that we can extend that period to nine weeks or even 12 weeks? People tend to breathe their head in the sand, and it is a great worry that people do not contact the organisations straight away. James Dornan mentioned the situation just now with the tax credits and Westminster, and I do not think that we can hide from that, Mr Roberts. It is not being political to mention that. I think that we have all got to work together in this chamber to ensure that people are aware that there is help out there for them, regardless of what the political situation is. I would like to say that we all agree that those organisations do a great job. We have to highlight and publicise them more, but perhaps we could extend the breathing space a wee bit, and I would look forward to the minister's reply in the summing up. Many thanks, and I now invite Fergus Ewing to respond to the debate minister. Seven minutes or so, please. I am delighted that James Dornan has given us the opportunity to debate the excellent work that the charity Step Change performs for people in Scotland and throughout the UK. Reference is made to the fact that Gillian Thomson of Step Change is listening to the debate, and she was the former accountant bankruptcy with whom I worked for many years. Sharon Bell, who also works with Step Change, used to be an adviser to the Scottish Government and sits at the seats up at the back in the debates that I have carried out since 2007. I want to focus on the work that Step Change has done and on its report and action plan on problem debt. I think that this is one of the best reports that I have seen for a long time, and it focuses on practical solutions to what I think is one of the most deep-seated and serious problems that is so often hidden from view in Britain. In the UK, over 2.4 million dependent children live in indebted households.  More than half of the children aged 10 to 17 are embarrassed because they lack the things that their peers have and nearly one in five have been bullied as a result. Step Change pointed out that personal credit debt in the UK stands at £168 billion. Debt is not a problem in itself. Debt is necessary for some purposes in life and where it is managed and controlled and affordable and repaid. It is necessary for many purposes, buying a house and buying a car. However, when it becomes a problem, I am afraid that things become very different indeed. The problem is very often not triggered by any fault, by proflegacy. The problem is very often delivered by things that occur in life, such as losing a job and being made redundant, such as illness in a family, such as relationship breakdown. That was evident to me in the days that are somewhat in the distant past now, when I was running a small legal practice and where I routinely acted for the debtor and focused in particular on specialising and trying to preserve the family home. That experience left its mark on me as explaining and giving me an insight into the human cost, the human misery of those problems. What is the step change in the report that we are recommending? We recommend that every family should have £1,000 in savings to cover a sudden cost or income shock. There are many shocks for people who have no spare cash. The washing machine breaks down. If you have children well, you need a washing machine. Go out and buy it with a payday loan can be the start of the problems. Mr Dornan gave one example of a payday loan. It sounds like an ambitious policy, but if you read the recommendations in step change report, they go some way to saying how it can be made to work through nudging and changing behaviour, deductions and linking it to the automatic payroll pension, I believe. That would not deal with self-employed, it would not deal with people below £10,000 income, but read the report because I think that it sets out a fascinating proposal that across the parties, I hope, will receive the attention that it deserves. To ensure that all low-income households can access low-cost credit products, step change, as James Dornan pointed out, advise a huge number of people, an enormous number of people in Scotland and the UK. In a great number of cases, their advice is efficacious. In other words, it works. Of course, not everybody takes advice, as I well remember. Many people choose to ignore it, but many people do and benefit from it, and their lives change for the better substantially. We want to scale up free advice so that it reaches the 1.4 million people who urgently need it. That is why, among the reforms that we have made, we need to make debt advice mandatory in certain circumstances. That has led in turn to, I think, a greater uptake of advice. To ensure that everyone dealing with their debt problem gets the protection against interest charges, enforcement and collections that they need. We have, in Scotland, taken forward the DAS, the Debt Administration Scheme proposal. I am not sure that they have brought a counterpart in England. It works well. It provides a diligence stopper. The fear of debt action being taken, the sheriff officers coming to the door, is a huge fear. Unless one has been there or has spoken to people directly who have been affected, it is difficult to understand that, in our comfortable lives, we are unaware of the pressures. Therefore, the DAS, the Dilligence Stopper of six weeks, provides a breathing space. Three members, I think, have said that maybe that should be extended. Let me confirm that we are undertaking a policy review of all the bad-ass—that is a piece of legislation, Presiding Officer—reforms, including the moratorium period, and that will take place next year. It is the bad-ass, as I should say. For the uninitiated, it is the bankruptcy and debt advice Scotland legislation. It just trips off the tongue, does it not? We need to protect children and families for the harm of aggressive debt collection practices. I was pleased that payday loans are now subject to caps of £15 default fee in 100 per cent interest, but, for goodness me, 100 per cent interest is that the right cap? I do not think so. The first debate that we had in this session of Parliament was on that topic, and I pressed the UK Government time and time again. Firstly, they said that they were not doing anything about it. Laterally they did, but I do not think that they or the FCA have gone far enough. I see that I am into my last minute. If step change did not exist, we would have to invent them. They are a great charity. They do terrific work. Mr Macintosh's suggestion or practice of referring a constituent to step change is one that we could emulate. Maybe we could encourage MSPs and MPs to do that, because they will receive good advice. We are doing a lot in education at the moment. We have a financial health service policy that 35,000 people have benefited from. We are working on credit union availability, about which I have 18 seconds to impart. Not enough, I am afraid, perhaps another day. In Scotland there is a broader consensus that the sort of recommendations from step change in this excellent report on action plan and problem debt are things that we want to do and we want to see happen. If we do them, even only partly, we will make a tremendous difference to the lives of many in this country, which are scarred by the misery of having a problem debt issue. That concludes James Dornan's debate on step change to debt charities action plan on problem debt. I now suspend this meeting until 2.30 p.m.