To determine which graph represents a function that has an inverse function, we must verify if the function passes the Horizontal Line Test. A function passes the Horizontal Line Test if every horizontal line intersects the graph at most once. This ensures the function is one-to-one and thus has an inverse.

Observing the Graphs:

1. Graph 1: The graph does not pass the Horizontal Line Test as horizontal lines intersect the curve more than once. This function does not have an inverse.
2. Graph 2: The graph is a straight line with a consistent slope. It passes the Horizontal Line Test, as any horizontal line will intersect it exactly once. This function has an inverse.
3. Graph 3: The graph fails the Horizontal Line Test because horizontal lines intersect the graph more than once. It does not have an inverse.
4. Graph 4: Similar to Graph 3, this graph also fails the Horizontal Line Test. It does not have an inverse.

Conclusion:

The correct answer is Graph 2, as it is the only function with an inverse.

Do you want further details or have any questions?

Related Questions:

1. Why does the Horizontal Line Test ensure the existence of an inverse function?
2. How do we determine if a line is one-to-one mathematically?
3. What transformations preserve the property of having an inverse?
4. Can a parabola ever have an inverse? If so, under what conditions?
5. What is the process of finding the equation for the inverse of a given function?

Tip: Always check if a function is one-to-one before attempting to find its inverse.