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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 \( y = x \).

Graph the inverse of the given function f from the provided graph.

Learn how to graph the inverse of a function by reflecting points across the line y = x. This example involves identifying key points on a graph, swapping x- and y-coordinates, and plotting the inverse.

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