what are the possible degrees for the polynomial function? degrees of 5 or greater odd degrees of 5 or…

Explanation:

Step1: Analyze the end - behavior

For a polynomial function (y = a_nx^n+\cdots+a_0), if (n) is even: when (a_n>0), (y\to+\infty) as (x\to\pm\infty); when (a_n < 0), (y\to-\infty) as (x\to\pm\infty). If (n) is odd: when (a_n>0), (y\to+\infty) as (x\to+\infty) and (y\to-\infty) as (x\to-\infty); when (a_n < 0), (y\to-\infty) as (x\to+\infty) and (y\to+\infty) as (x\to-\infty). In the given graph, as (x\to-\infty), (y\to-\infty) and as (x\to+\infty), (y\to-\infty), so the degree (n) is even.

Step2: Analyze the number of turning points

The maximum number of turning points of a polynomial function is (n - 1). The given graph has at least 5 turning points. If (n-1\geq5), then (n\geq6)

Answer:

even degrees of 6 or greater