Questions: Determine if the graph can represent a polynomial function. If so, assume that the end behavior and all turning points are represented in the graph.

Solution Steps

The graph is smooth and continuous. It has two turning points. As _x_ approaches negative infinity, _y_ approaches negative infinity. As _x_ approaches positive infinity, _y_ approaches positive infinity.

Since the graph is smooth, continuous, and has turning points as its only discontinuities in the derivative, it could represent a polynomial.

The graph displays two turning points. A polynomial of degree _n_ has at most _n_-1 turning points. Therefore, this graph could represent a 3rd-degree polynomial or higher.

Final Answer: The graph could represent a polynomial function, specifically a polynomial of degree 3 or higher.