Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 5 - Polynomials and Polynomial Functions - 5-1 Polynomial Functions - Lesson Check: 5

Answer

The end behavior of the graph of the given function is: $\underline{\text{up and down}}$

Work Step by Step

The end behavior of the graph of a polynomial function is dependent on the polynomial's degree and leading coefficient. (i) When the degree is even and the leading coefficient is positive, the end behavior of the graph is up and up; (ii) When the degree is even and the leading coefficient is negative, the end behavior of the graph is down and down; (iii) When the degree is odd and the leading coefficient is positive, the end behavior of the graph is down and up; and (iv) When the degree is odd and the leading coefficient is negative, the end behavior of the graph is up and down The given polynomial function has a degree of 7 and a leading coefficient of -2. Thus, the end behavior of its graph is: $\underline{\text{up and down}}$.
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