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To graph the inverse \( f^{-1} \) of the given function \( f \), you can follow these steps:

1. **Understand the nature of an inverse function**: 
   The graph of the inverse function \( f^{-1} \) is a reflection of the graph of \( f \) over the line \( y = x \). This means that for every point \( (x, y) \) on the graph of \( f \), the corresponding point \( (y, x) \) will be on the graph of \( f^{-1} \).

2. **Identify key points on the graph of \( f \)**: 
   From the image you uploaded, identify points such as \( (0,0) \), \( (2,4) \), \( (3,8) \), etc., as examples of points on the graph of \( f \). The inverse function will have the corresponding points \( (0,0) \), \( (4,2) \), \( (8,3) \), etc.

3. **Reflect the graph across the line \( y = x \)**: 
   Plot the reflected points from step 2 on the new graph and connect them accordingly to match the shape of the original function, but reflected.

### Would you like further assistance with plotting this inverse graph or any details on how to proceed? Let me know!

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Here are 5 related questions to explore this further:

1. How does the process of finding the inverse function differ algebraically from graphing it?
2. What is the relationship between the domain and range of \( f \) and \( f^{-1} \)?
3. What are the conditions for a function to have an inverse (bijectivity)?
4. How can you verify if two functions are inverses of each other algebraically?
5. How does the derivative of a function relate to the derivative of its inverse?

**Tip:** Always ensure that the function you're dealing with is one-to-one before finding its inverse, which means each \( y \)-value is associated with exactly one \( x \)-value.

Graph f^{-1}, the inverse of the given function f.

Learn how to graph the inverse function f^{-1} by reflecting the original function over the line y = x. This involves identifying key points on the original graph and plotting their reflections. Suitable for students in Grades 9-12, this exercise covers inverse functions and graph transformations.

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