While studying graph transformations I came across horizontal and vertical scale and translations of functions. I understand the ideas below.
- $f(x+a)$ - grouped with x, horizontal translation, inverse, x-coordinate shifts left, right for -a
- $f(ax)$ - grouped with x, horizontal scaling, inverse so x-coordinate * 1/a
- $f(x)$ + a - not grouped with x, vertical translation, shifts y-coordinate up, d
- $af(x)$ - not grouped with x, vertical scaling, y-coordinate * a
I have mostly memorized this part but I am unable to figure out why the horizontal transformations are reversed/inverse?
Thanks for your help.