jmc

For every point $(x,y)$ on the graph of $y=f(x)$, we know $(2-x,y)$ is also on the graph of $y=f(x)$.

We have $x=1+(x-1)$ and $2-x=1-(x-1)$, so the geometric transformation which takes $(x,y)$ to $(2-x,y)$ is reflection across the vertical line $\boxed{x=1}$.