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$f(x) = 2-4\cos(2x-\frac{1}{3}\pi)$

How do you get this function from as standard function?

My answer:

$ y = \cos x $

↓ Multiply with the x-axis, -4

$y=-4\cos x$

↓ Multiply with the y-axis, 0.5

$y=-4\cos 2x $

↓ Translation $(\frac{1}{6}\pi, 2)$


Is this answer correct? The only part I am really concerned about is the final translation, with the $(\frac{1}{6}\pi)$ instead of $(\frac{1}{3}\pi)$.

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If you don't want bad answers, I might ask you first of all not to post a bad question. What on earth does "multiply with the x-axis" mean? Are you stretching along the x-axis? Are you keeping the x-axis fixed and stretching vertically? Anyway, your final translation looks right. –  Billy Sep 17 '12 at 16:43
I agree with @Billy that the question is rude. We could simply answer that this site is not for private lessons. If "help" means "do whatever I ask and shut up" for ZafarS, he/she should open a good english dictionary and look up that word. –  Siminore Sep 17 '12 at 17:08
ZafarS, not to gang up on you, or anything, but I agree with the above two points – there's really no reason why we should help, except that we enjoy it, so your tone is a little demanding. You're welcome to ask that people answer in a particular way, but if they want to answer in a different way, that's really up to them. –  Ben Millwood Sep 17 '12 at 17:35
I'm sorry guys, I was kind off in a bad mood when I asked it. I've got a big test coming up tomorrow and I missed all lessons because of an illness so I basically have to use you guys as my teachers. Also, 'multiply with the x-asis', in my language it is called that, I thought (like often) that I could just directly translate it into english and it would still be understandable, guess not.. –  ZafarS Sep 17 '12 at 19:35

1 Answer 1

up vote 1 down vote accepted

$\frac\pi6$ seems to be correct:

You have to consider first, what is happening in 'machine' $\cos$ with your variable $x$. Those that happen before applying $\cos$ will take action horizontally and inverted.

  • First plot $\cos x$,
  • then $\cos(x-\frac\pi6)$ -- [shift to the right by $\frac\pi6$]
  • then $\cos(2x-\frac\pi3)$ -- [shrink horizontally by $1/2$]
  • then $-4\cos(2x-\frac\pi3)$ -- [reflect along the x-axis because of the $-$ and multiply vertically by 4]
  • finally add 2 -- [vertically]
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