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?
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 $$f(x)\to f(x-c)\to f(c-x)\to f(2c-x)$$