Question

In a polynomial function, the degree of the function tells us key information about the graph. Which of the following is NOT true?

A) The maximum number of turning points is one less than the degree.
B) If the degree is even, both ends of the graph are pointing in the same direction.
C) An even degree reveals the right side of the graph is pointing up.
D) The number of roots matches the degree.

Answer 1

The incorrect statement about polynomial functions is C) An even degree reveals the right side of the graph is pointing up, because even-degree polynomials can point down if the leading coefficient is negative.

Step-by-step explanation:

The statement that is NOT true about the degree of a polynomial function and its graph is C) An even degree reveals the right side of the graph is pointing up. The degree of a polynomial function does indeed provide key information about its graph:

• The maximum number of turning points is one less than the degree of the function.
• If the degree is even, both ends of the graph point in the same direction, either up or down based on the leading coefficient's sign.
• The number of potential roots (including complex roots) of the polynomial equals the degree of the function.

However, option C is not always true because an even-degree polynomial can point down on the right side if the leading coefficient is negative.