Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 2 - Nonlinear Functions - 2.3 Polynomial and Rational Functions - 2.3 Exercises - Page 74: 22

Answer

* Because the range is $(-\infty, \infty)$ this must be a polynomial of odd degree. * Notice also that the polynomial becomes a large positive number as $x$ becomes a large positive number, so the leading coefficient must be positive . * Finally, notice that it has four turning points and we know that a polynomial of degree $n$ has at most $n-1$ turning points. So the polynomial graphed in the Figure might be degree $5$, although it could also be of degree $7, 9,$ etc.

Work Step by Step

* Because the range is $(-\infty, \infty)$ this must be a polynomial of odd degree. * Notice also that the polynomial becomes a large positive number as $x$ becomes a large positive number, so the leading coefficient must be positive . * Finally, notice that it has four turning points and we know that a polynomial of degree $n$ has at most $n-1$ turning points. So the polynomial graphed in the Figure might be degree $5$, although it could also be of degree $7, 9,$ etc.
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