How do I reflect a function about a specific line? Starting with the graph of $f(x) = 3^x$, write the equation of the graph that results from reflecting $f(x)$ about the line $x=3$.
I thought that it would be $f(x) = 3^{-x-3}$ (aka shift it three units to the right and reflect it), but it's wrong.
The right answer is $f(x) = 3^{-x+6}$ but I just can't get to it!
An explained step by step would be appreciated so I can follow what is being done.
Thanks in advance!

Your idea will work if you just carry it fully through. First shift three units to the left, so the line of reflection becomes the y axis, then flip, and finally remember to shift three units back to the right to put the center line back where it belongs.
(This gives the $f(6-x)$ solution you already know).
