To determine if a graph represents a function that has an inverse function, you can use the Horizontal Line Test. This test states that if any horizontal line intersects the graph more than once, then the function does not have an inverse function.
In your description, the graph:
- Falls through quadrant 2
- Has a minimum in quadrant 3
- Rises through the origin
- Has a maximum in quadrant 1
- Falls through quadrant 4
Given this behavior, it sounds like the graph goes up and down before returning to the x-axis, which implies that some horizontal lines drawn through the graph could potentially intersect it at more than one point.
Since the graph does not appear to be one-to-one (a requirement for a function to have an inverse), the answer is:
No. The graph does not represent a function that has an inverse function.