# Mirror a function about x = c axis

I'm trying to mirror a function $f(x)$ about the $x=c$ axis. To mirror it about the $x=0$ axis you just have to plot $f(-x)$.

I tried to mirror $f(x) = x^2$ about the $x = c$ axis. And I found that the mirrored function of $f$ is $(x-2c)^2$.

This just works for the $x^2$ function, but I need to mirror any function. How to do that?

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In general, $f(x)$ mirrored across the line $x=c$ is simply $f(2c-x)$. To see this, note that we can mirror $f(x)$ by translating it down by $c$, flipping it and then translating it back up by $c$, which gives $$f(x)\to f(x-c)\to f(c-x)\to f(2c-x)$$
Thanks! Do you know how to mirror across the line $y=c$? –  Cobold May 25 '12 at 21:58
@Cobold The situation is almost identical. Just translate along the $y$ axis instead of $x$. –  Alex Becker May 25 '12 at 21:59
This can be simply evaluated by shifting the function by $c$ units towards negative x-axis or in transformation terms $f(x) \rightarrow f(x+c)$ ,finding the mirror image of this new curve along $x=0$, i.e $f(x+c) \rightarrow f(-x+c)$ and then re-shifting the new curve by $c$ units towards right i.e $f(-x+c) \rightarrow f(2c-x)$.Conclusively, the mirror image of any curve $y=f(x)$ about $x=c$ would be given by $y=f(2c-x)$.