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).

  • 1
    $\begingroup$ What if I wanted to reflect it on the curve $ g \left( x \right) = x $? $\endgroup$
    – Royi
    Nov 8 '15 at 1:46
  • $\begingroup$ Reflecting a function along the line y = x is the same as computing the inverse of the function. So use a method for computing the inverse of a function to find the reflection about the line y = x. $\endgroup$
    – user10
    Feb 18 '20 at 21:23

Replace $x$ with $6-x$. This works because if $x=3+t$, then $6-x=3-t$.

Or, in words: if $x$ is $t$ units to the right from $3$, then $6-x$ is $t$ units to the left from $3$.

  • $\begingroup$ I see that in essence x is replaced with 6-x, but how would I go about determining that is what needs to be done? $\endgroup$
    – kubasub
    Sep 12 '11 at 20:09
  • $\begingroup$ @Jakub, please see my edit. $\endgroup$
    – Rasmus
    Sep 12 '11 at 20:11

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.