Question

1. if the graph of a polynomial function has 3 turning points, what is the minimum degree of the function?

Explanation:

Step1: Recall the turning points rule

For a polynomial function, the maximum number of turning points is given by \(n - 1\), where \(n\) is the degree of the polynomial. To find the minimum degree for a given number of turning points, we use the fact that if there are \(t\) turning points, the minimum degree \(n\) satisfies \(n-1\geq t\), so \(n\geq t + 1\).

Step2: Apply the rule to the problem

We are given that there are 3 turning points. Using the formula \(n\geq t + 1\), where \(t = 3\), we substitute \(t\) into the formula: \(n\geq3 + 1=4\). So the minimum degree is 4.

Answer:

4