move it, shift it, TRANFORM IT!


section13: compound transformation
now that you've learnt the basics, it's time to integrate all those skills and do compound transformations! compound tranformation, as the name suggests, is doing a few transformations together. you basically just have to transform step by step.
let's take graph of y=f(3x +1).
1st, you start off with the graph of y=f(x).
then, do the y=f(x+1) transformation. i.e. shift the graph to the left by 1 unit.
in this case, the x-coordinates become x=0 and x=4.

next, do the y=f(3x) transformation. i.e. multiply the x-coordinates by 1/3.
now the x-coordinates will be x=0 and x=4/3.

and there you go, your y=f(3x+1) graph! simple enough right?
here we have another example:
y=f(3x+1)
by doing the following steps, you will be able to attain this graph:
y=f(3x)

y=f(x)

y=f(3x+1)

note that the compound transformations for x-variables and y-variables are different.
in the case of x-variables, always translate before scaling or reflecting.
in the case of y-variables, always scale or reflect before translating.
OHYES LAST SECTION! aren't you just glad?! i'm gladder xD transformation isn't that difficult after all isn't it? ok enough small talk, last question!
oo new graph!! let's transform graph of y=p(x) to graph of y=1/2p(2x-1).
quite a mouthful, but digest, analyse and choose the correct answer! (it might help if you sketch the steps yourself)