A Function and Its Inverse on the Graph — Cheat sheet

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Key method

If $(a,b)$ lies on a bijective function's graph, $(b,a)$ lies on its inverse graph. Vertical and horizontal features exchange: domain becomes range, and a vertical asymptote becomes a horizontal one where applicable.

Example

The exponential $y=2^x$ passes through $(0,1)$ and $(1,2)$ . Its inverse $y=\log_2 x$ passes through $(1,0)$ and $(2,1)$ . The exponential's horizontal asymptote $y=0$ corresponds to the logarithm's vertical asymptote $x=0$ .

Avoid this mistake

A graph and its inverse need not meet on the displayed window. Reflection does not mean reflection across the vertical axis.