Question

The graph of a polynomial function continues down on the left and continues up on the right. Which of the following must be true about this polynomial function?

a The function is even, with a positive leading coefficient. b The function is odd, with a positive leading coefficient. c The function is even, with a negative leading coefficient. d The function is odd, with a negative leading coefficient.

Answer 1

The given information that the graph of a polynomial function continues down on the left and continues up on the right is an indication that the degree of the polynomial is odd.

If the degree of the polynomial is odd, then the leading coefficient must be either positive or negative depending on the end behavior of the graph.

Since the graph continues down on the left and up on the right, the end behavior indicates that the leading coefficient is negative.

Therefore, the only option that satisfies the given information is:

d) The function is odd, with a negative leading coefficient.