Reflect an exponential graph to define the logarithm

The Teacher writes $y=f(x)\Rightarrow f^{-1}(y)=x$, $y=e^x$, $x=\ln y$, so $f^{-1}(y)=\ln y$. Since $R_f=(0,\infty)$, $D_{f^{-1}}=(0,\infty)$. Rename the input and give the rule together with that domain. Independently the inverse range is all real numbers.

The Teacher completes all three curves, labels the two intercepts, the horizontal asymptote $y=0$ of the exponential and the vertical asymptote $x=0$ of the logarithm. Use equal unit scales on both axes so reflection in $y=x$ is geometrically correct. The later source illustration also shows $(1,e)$ and its reflected point $(e,1)$; these are included in the same reconstruction with dashed coordinate guides. In general $(a,b)$ becomes $(b,a)$, horizontal asymptotes become vertical, and vertical become horizontal. Draw $y=x$ to show the relationship even when a sketch question does not request that reference line explicitly.