Question

question #10 given the graph below, what would be the minimum degree of the polynomial? o 4 o 6 o 1 o 3

Explanation:

Step1: Recall polynomial - degree rule

The minimum degree of a polynomial is related to the number of turning points. The number of turning points \(T\) of a polynomial function \(y = f(x)\) satisfies the inequality \(T\leq n - 1\), where \(n\) is the degree of the polynomial.

Step2: Count turning points

Count the number of turning - points of the given graph. A turning point is a point where the graph changes from increasing to decreasing or vice - versa. The graph has 3 turning points.

Step3: Determine minimum degree

Using the formula \(T\leq n - 1\), if \(T = 3\), then \(3\leq n - 1\). Solving for \(n\) gives \(n\geq4\). So the minimum degree of the polynomial is 4.

Answer:

4