1. The problem asks if the given graph represents a function that has an inverse function. 2. A function has an inverse if and only if it is one-to-one (passes the Horizontal Line Test). 3. The graph is a downward-opening parabola, which is symmetric and not one-to-one over its entire domain. 4. Therefore, the parabola does not have an inverse function over all real numbers. 5. However, if we restrict the domain to one side of the vertex, the function can have an inverse on that restricted domain. 6. In summary, the given parabola does not have an inverse function without domain restriction.