https://file.aiquickdraw.com/mathbot/file/1726587363692xvwdk6zy.jpg

The graph provided appears to be the graph of a function that increases steadily but flattens at certain points before continuing upward. To determine whether the inverse of this function is also a function, we can apply the **horizontal line test**.

### Horizontal Line Test:
- A function has an inverse that is also a function if **no horizontal line intersects the graph at more than one point**. 
- If any horizontal line crosses the graph at more than one point, then the function does **not** pass the test, and the inverse is **not a function**.

### Applying the Test to the Given Graph:
- From the image, there are sections where the graph seems to flatten or level out, which suggests that a horizontal line could intersect the graph at multiple points in these regions. For instance, around \( y = 4 \), a horizontal line could intersect the graph in more than one place.
- Therefore, the function does **not** pass the horizontal line test.

### Conclusion:
The inverse of the function shown is **not a function**, because the original function fails the horizontal line test (it is not one-to-one).

Would you like more details or have any questions?

Here are 5 related questions:
1. How does the vertical line test determine if a graph is a function?
2. Can a function have an inverse if it fails the horizontal line test?
3. What are the implications of a function being one-to-one?
4. How can you algebraically find the inverse of a function?
5. How can transformations affect the graph of a function and its inverse?

**Tip:** For a function to have an inverse that is also a function, it must be one-to-one, meaning each \( y \)-value corresponds to exactly one \( x \)-value.

Is the inverse of the function shown below also a function? Explain your answer.

This question examines whether the inverse of a given function is also a function. By applying the horizontal line test, it is determined that the inverse of the function shown fails the test and is therefore not a function. This problem involves key mathematical concepts such as inverse functions, one-to-one functions, and the horizontal line test, and is suitable for students in Grades 10-12.

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