Question

determine whether or not the graph shown is the graph of a polynomial function.

not a polynomial function
polynomial function

Explanation:

Identify polynomial graph properties

Using the Polynomial Functions knowledge point

A polynomial function's graph must be continuous (no breaks, holes, or asymptotes) and smooth (no sharp corners or cusps).

Analyze the given graph

The displayed curve is continuous across its entire domain and has smooth, rounded turns without any sharp corners, breaks, or gaps.

Determine the classification

Since the graph is both smooth and continuous, it represents a polynomial function.

Answer:

• not a polynomial function
• polynomial function (Correct answer)