Describing Inverses of Functions

To determine the inverse of the function, we first have to find the equation of the given graph. From the diagram, we see that the graph is a straight line which means we can write it on Slope-Intercept Form. $$\begin{array}{r}y=mx+b\end{array}$$ In this form, $m$ is the lines slope and $b$ is the $y$-intercept.

From the graph, we can identify the $y$-intercept as $b=\text{-}4$ and the slope as $m=\frac{2}{2}=1.$ $$\begin{array}{r}y=1\cdot x+(\text{-}4)\iff y=x-4\end{array}$$ By solving this equation for $x,$ and switching the roles of $x$ and $y,$ we can identify the inverse. Finally, to find the inverse, we change the roles of $x$ and $y.$ $$\begin{array}{rl}\text{inverse:}& x=y+4\\ \text{switch }\mathbf{x}\text{ and }\mathbf{y}\text{:}& y=x+4\end{array}$$ The inverse function is $y=x+4.$