Question

question #6 given the graph below, what would be the minimum degree of the polynomial? 5 2 4 3

Explanation:

Step1: Recall the relationship between degree and turning - points

The maximum number of turning - points of a polynomial function $y = f(x)$ is $n - 1$, where $n$ is the degree of the polynomial.

Step2: Count the turning - points

Count the number of turning - points on the graph. A turning - point is a point where the graph changes from increasing to decreasing or vice - versa. The given graph has 4 turning - points.

Step3: Determine the minimum degree

Since the maximum number of turning - points is $n - 1$, if there are 4 turning - points, then $n-1\geq4$. Solving for $n$, we get $n\geq5$. So the minimum degree of the polynomial is 5.

Answer:

5