The graph you provided shows the entire function $f$, and you are asked to graph $f^{-1}$, the inverse of $f$.

How to Graph the Inverse:

To graph the inverse function $f^{-1}(x)$, you reflect the graph of $f(x)$ over the line $y = x$. For each point $(x, y)$ on the graph of $f(x)$, the corresponding point on the graph of $f^{-1}(x)$ will be $(y, x)$.

Steps:

1. Identify key points on the graph of $f(x)$:

   • For example, if $f(0) = 2$, then $f^{-1}(2) = 0$.
   • Similarly, if $f(3) = 5$, then $f^{-1}(5) = 3$.

2. Plot the points for the inverse:

   • Take several points from the graph and swap the coordinates.

3. Draw the reflected graph:

   • After plotting the points, connect them in the same pattern but now reflected across the line $y = x$.

Would you like me to provide a step-by-step breakdown of some points and their reflections for this graph? Feel free to ask for further details.

Here are 5 questions to expand on the concept:

1. How can you confirm if two functions are inverses of each other?
2. What properties must a function have for its inverse to be a function as well?
3. What is the graphical significance of the line $y = x$ in finding inverses?
4. Can all functions have inverses? Why or why not?
5. How can you algebraically determine the inverse of a function if given the formula of $f(x)$?

Tip: Remember, a function must be one-to-one (each $y$-value has only one corresponding $x$-value) for it to have an inverse function.