https://file.aiquickdraw.com/mathbot/file/1730139321370cy0csc1k.jpg

To determine which graph has an inverse function, we need to see if each graph passes the **Horizontal Line Test**. The Horizontal Line Test states that a function has an inverse if any horizontal line intersects the graph at most once. This ensures the function is one-to-one, a necessary condition for it to have an inverse.

### Analysis of Each Graph:
1. **Graph 1**: This graph does not pass the Horizontal Line Test since horizontal lines intersect it more than once in some places (indicating it is not one-to-one). Therefore, it does not have an inverse.
  
2. **Graph 2**: This graph is a straight line with a positive slope, which is a one-to-one function. It passes the Horizontal Line Test, meaning it has an inverse.
  
3. **Graph 3**: This graph fails the Horizontal Line Test, as horizontal lines will intersect the curve multiple times in certain areas. Thus, it does not have an inverse.

4. **Graph 4**: Similarly to Graph 3, this graph also fails the Horizontal Line Test because horizontal lines can intersect it at multiple points. Therefore, it does not have an inverse.

### Conclusion:
**Only Graph 2 has an inverse function.**

Would you like further details or have any questions?

### Related Questions:
1. What makes a function pass the Horizontal Line Test?
2. How do you find the inverse of a linear function like the one in Graph 2?
3. Why is it important for a function to be one-to-one to have an inverse?
4. How can you determine the inverse of a function algebraically?
5. Can a function with a restricted domain have an inverse even if it originally fails the Horizontal Line Test?

### Tip:
For a function to have an inverse, make sure it passes both the **Vertical Line Test** (to be a function) and the **Horizontal Line Test** (to be one-to-one).

Understand how to determine if a function has an inverse by applying the Horizontal Line Test. This guide analyzes graphs, helping students identify which functions are one-to-one and have inverses, focusing on essential concepts for high school math.

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