https://file.aiquickdraw.com/mathbot/file/1725985080389qlr5op0j.jpg

To determine which function has an inverse that is also a function, we use the **Horizontal Line Test**. A function passes this test if no horizontal line crosses the graph more than once. If a function passes this test, its inverse will also be a function.

Let's analyze each graph:

1. **Top-left graph**: This graph fails the horizontal line test because a horizontal line will intersect it more than once at several places.
2. **Top-right graph**: This graph passes the horizontal line test. Any horizontal line will intersect it at only one point, meaning its inverse will also be a function.
3. **Bottom-left graph**: This graph fails the horizontal line test as a horizontal line can intersect it at more than one point.
4. **Bottom-right graph**: This graph also fails the horizontal line test. A horizontal line will intersect it in two places at many points.

**Conclusion**: The top-right graph is the one that has an inverse that is also a function.

Would you like more details or have any questions?

Here are 5 related questions for further learning:
1. What does it mean for a function to be "one-to-one"?
2. How can you determine if a function is invertible from its equation alone?
3. What is the algebraic process to find the inverse of a function?
4. Can functions that fail the horizontal line test be modified to have inverses?
5. How does the concept of domain restriction affect the invertibility of functions?

**Tip**: Always apply the horizontal line test before finding the inverse of a function to ensure the result is also a function!

Which function has an inverse that is also a function?

This problem explores how to determine which graph represents a function with an inverse that is also a function. The key concept is the Horizontal Line Test, which helps identify whether a function is one-to-one. Suitable for students in Grades 9-12.

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