Graphs of polynomial

Which of the following terms, when added to the given polynomial, will change the end behavior? y = -2x7 + 5x6 - 24

-x^8 and 5x^7

What are the possible degrees of the polynomial function in the graph?

4 6 8

Which of the following statements are true about graphs of polynomial functions? Check all that apply.

A and B

A local zoologist presents a graph of a primate population and describes the characteristics as follows: Which graph best represents the population described?

C

What are the possible degrees for the equation of this graph?

Even degrees of four or greater

A function is a fifth-degree polynomial. How many turning points can it have?

Four or less

The equation for this graph has a leading coefficient that is

Negative

The sign of the leading coefficient for the polynomial equation of the graph is . This graph has _____turning point(s). Possible degrees for this graph include:

Negative 1 4 and 6

What is the end behavior of this function?

Negative infinity

The addition of either -x8 or 5x7 will change the end behavior of y = -2x7 + 5x6 - 24. Explain how each of the added terms above would change the graph.

The degree is odd, so the graph has ends that go in opposite directions. A negative coefficient means the graph rises on the left and falls on the right. Adding -x8 changes the degree to even, so the ends go in the same direction. Adding 5x7 changes the leading coefficient to positive, so the graph falls on the left and rises on the right.