How to define new function by stretching and shifting a function?

Question

I realize this could be an easy problem but I'm going to ask anyway: I am given a function and I need to stretch it horizontically and vertically then to shift it to the left. I know how to define new functions based on another but this one has trigonometry in it and that's confusing me pretty much.

Any help would be appreciated :)

Answer 1

With some inequalities based on assuming a "stretch" makes distances bigger:

You want $af(bx+c)$ with $|a|>1$ for a vertical stretch (with $a<0$ if you want to vertically invert the function), $|b|<1$ for a horizontal stretch (with $b<0$ to horizontally flip), and $c/b>0$ for a leftward shift.