To graph the inverse of the given curve, you will need to reflect it over the line $y = x$. This means that for each point on the original graph, its coordinates $(x, y)$ will be swapped to become $(y, x)$ in the inverse. Here’s how you can proceed:

1. Identify Points on the Original Curve: Select a few points on the given graph. For example:

   • Point 1: $(0, -5)$
   • Point 2: $(1, -3)$
   • Point 3: $(4, 0)$
   • Point 4: $(6, 2)$
   • Point 5: $(8, 4)$

2. Swap Coordinates: For each point $(x, y)$ on the original curve, plot the point $(y, x)$ to reflect it over the line $y = x$.

   • Inverse of Point 1: $(-5, 0)$
   • Inverse of Point 2: $(-3, 1)$
   • Inverse of Point 3: $(0, 4)$
   • Inverse of Point 4: $(2, 6)$
   • Inverse of Point 5: $(4, 8)$

3. Plot the Reflected Points: Mark these new points on the graph and connect them smoothly to mirror the shape of the original graph on the opposite side of the line $y = x$.

4. Draw the Inverse Curve: Connect the points in a way that maintains the general shape and curvature of the original graph but mirrored across $y = x$.

If you need further assistance plotting these points or interpreting this reflection, let me know!

Would you like a more detailed explanation of this process, or do you have any specific questions?

Here are some related questions to expand your understanding:

1. Why does swapping $x$ and $y$ values reflect a point over the line $y = x$?
2. How can you determine if a function has an inverse graphically?
3. What does it mean for a function to be invertible?
4. How do horizontal and vertical line tests relate to invertibility?
5. What are the practical applications of finding the inverse of a function?

Tip: When plotting an inverse, always check if the original graph passes the horizontal line test, ensuring each $y$-value corresponds to only one $x$-value.