Question

a polynomial function is graphed. which of the following choices could be the degree of the polynomial? 1 3 4 7

Explanation:

Step1: Recall polynomial - degree rules

The number of turning points of a polynomial function \(y = f(x)\) is at most \(n - 1\), where \(n\) is the degree of the polynomial. A turning - point is a point where the graph changes from increasing to decreasing or vice - versa.

Step2: Count turning points

Count the number of turning points on the given graph. The graph has 3 turning points.

Step3: Determine possible degrees

Since the number of turning points \(T=n - 1\) (at most), if \(T = 3\), then \(n=T + 1=4\) or \(n>4\) (because the number of turning points is at most \(n - 1\)). A first - degree polynomial (\(n = 1\)) has 0 turning points, and a third - degree polynomial (\(n = 3\)) has at most 2 turning points. A seventh - degree polynomial has at most 6 turning points, but 4 is the smallest degree that can have 3 turning points.

Answer:

C. 4