https://file.aiquickdraw.com/mathbot/file/1728103472445dn2d53jl.jpg

The image shows a linear graph of a function \( f(x) \), and the task is to draw the graph of its inverse function \( f^{-1}(x) \).

### Steps to graph the inverse of a function:
1. **Reflect the graph over the line \( y = x \)**: The graph of the inverse function is a reflection of the original function across the line \( y = x \).
2. **Swap the coordinates**: For each point \( (x, y) \) on the original graph, the corresponding point on the inverse graph will be \( (y, x) \).

#### Graph details:
- The line passes through key points such as \( (0, 0) \), \( (1, 2) \), and \( (2, 4) \).
- For the inverse, swap these points: 
  - \( (0, 0) \) remains unchanged.
  - \( (1, 2) \) becomes \( (2, 1) \).
  - \( (2, 4) \) becomes \( (4, 2) \).

### Drawing the inverse:
- Plot the points \( (0, 0) \), \( (2, 1) \), \( (4, 2) \), and extend the line accordingly.
- Ensure the line is symmetric about \( y = x \).

Would you like further details or explanations? 

Here are 5 related questions:
1. How do we verify if two functions are inverses of each other?
2. What is the general process for finding the inverse of a linear function algebraically?
3. How do inverse functions relate to one-to-one functions?
4. Can a function always have an inverse?
5. How does the domain and range of a function change when finding its inverse?

**Tip:** Always check if a function is one-to-one before finding its inverse; only one-to-one functions have inverses.

Use the graph of f to draw the graph of its inverse function.

Learn how to graph the inverse of a linear function by reflecting the original function's graph over the line y = x. This problem includes step-by-step instructions for swapping coordinates and plotting the inverse.

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