# Graph transformations.

This is the exact problem from the worksheet. Now I understand that it is giving the parent function for $f(x)$. The only formula I know of for transformations is $y=f(x)\rightarrow y=af(bx+c)+d$ where:
$a$=vertical compression or expansion
$b$=horizontal compression or expansion
$c$=left or right(+=left, -=right)
$d$=up or down (+=up, -=down)
This is all the information I have for transformations. I have done a lot of them.

Edit: I solved the first two and now need a clearer explanation on $c$ and $d$. No answers please.

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so set $a=1,b=-1,c=0,d=0$. You'll get a mirror effect on the vertical axis for (b) since for $x=-2$ you will get $f(2)=0$. – Raymond Manzoni Aug 7 '12 at 19:56
hint for (d) : is there a way (choice of $x$) to see the left part of the picture? (your (c) in the other comment is right) – Raymond Manzoni Aug 7 '12 at 20:03
What do you mean by "is there a way of seeing the left part of the picture"? Do you mean left of the $x$-axis? – Austin Broussard Aug 7 '12 at 20:07
the part $x<0$ of your initial picture – Raymond Manzoni Aug 7 '12 at 20:08
in practice yes (for (c) the mirror effect is around the $y=0$ for $x<0$)). For other graphs the right part could be changed and the left part not mirrored... – Raymond Manzoni Aug 7 '12 at 20:40

As with your earlier question, look at what $f(-x)$ means: it means compute $f$ at a value of $-x$.

In the graph shown above, your function $f$ appears to be defined for all $x \in [-2,2]$, meaning that for every $x$ where $f$ is defined, then it is also defined at $-x$.

So, if you want to compute $f(-x)$ when $x = 1$, this is exactly the value of $f(-1)$.

This means that $f(-x)$ would then reflect this graph about the $y$-axis.

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Okay, got it. So now onto $c$ and $d$. They are indeed different but how? For $c$, the whole function is in the absolute value bars; but in $d$, it is just the $x$ value. Can you please shed some light on this but do not give me the answer. Thanks – Austin Broussard Aug 7 '12 at 19:57
As always, start by computing the value of the function argument, then use your graph to figure out what the value of that function is at that point. If I said $banana = 2$, then what is $f(banana)$? Now if I say what is $|x|$ when $x = 2$, can you tell me what $f(|x|)$ is? – Emily Aug 7 '12 at 20:09
It would be $2$, right? – Austin Broussard Aug 7 '12 at 20:11