## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

The graphs of $f$ and $f^{-1}$ (if the inverse is defined) are symmetrical about the line $y=x.$ Symmetry: Reflection of the point (a,b) about the line $y=x$ is the point (b,a). The graph of $f(x)=x^{3}+1$ passes the horizontal line test, (as in example 8, the graph of $y=x^{3}$ is raised up by 1 unit) so $f^{-1}(x)$ exists. Graph $f$ by creating a table of function values: $\left[\begin{array}{lllllll} x & -2 & -1 & 0 & 1 & 2 & \\ y=f(x) & -7 & 0 & 1 & 2 & 9 & \end{array}\right]$ Join the points with a smooth curve (blue graph). To graph $f^{-1}(x)$we plot the points $(y,x)$ from the above table. Join the points with a smooth curve (red graph)