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).