To graph the inverse of the given function $f$, we need to reflect the graph of $f$ across the line $y = x$. This means swapping the $x$- and $y$-coordinates of each point on the graph of $f$. Let’s break down the process:

1. Identify key points on the graph of $f$. From the image, I can roughly estimate the following points on the graph of $f$:

   • $(-6, -5)$
   • $(-2, 0)$
   • $(0, 2)$
   • $(4, 6)$
   • $(6, 8)$

2. Swap the coordinates of each point to get the points on the inverse function $f^{-1}$:

   • $(-6, -5) \rightarrow (-5, -6)$
   • $(-2, 0) \rightarrow (0, -2)$
   • $(0, 2) \rightarrow (2, 0)$
   • $(4, 6) \rightarrow (6, 4)$
   • $(6, 8) \rightarrow (8, 6)$

3. Plot these new points:

   • Plot $(-5, -6)$
   • Plot $(0, -2)$
   • Plot $(2, 0)$
   • Plot $(6, 4)$
   • Plot $(8, 6)$

4. Draw the graph: Connect these points smoothly to represent the inverse function. The graph should resemble the original function but flipped across the line $y = x$.

Would you like more details on how to reflect a graph across the line $y = x$ or how to plot these points precisely? Let me know if you'd like me to clarify any steps!

Here are 5 related questions to explore:

1. How do you find the inverse of a function algebraically?
2. What properties do a function and its inverse share?
3. What is the relationship between the slopes of a function and its inverse at corresponding points?
4. How can you verify that a function is invertible?
5. How does restricting the domain of a function affect its inverse?

Tip: The graph of a function and its inverse are symmetrical with respect to the line $y = x$.