Graphs of Inverse Functions

If $f$ is bijective (one-to-one and onto) with inverse $f^{-1}$, then $y=f(x)$ exactly when $x=f^{-1}(y)$. So the point $(a,b)$ lies on the graph of $f$ if and only if the point $(b,a)$ lies on the graph of $f^{-1}$ — every point's coordinates are simply swapped.

Geometrically, swapping the coordinates of every point on a curve is exactly the same as reflecting the curve in the line $y=x$. So: