Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 3 - Polynomial and Rational Functions - Section 3.1 Polynomial Functions and Models - 3.1 Assess Your Understanding - Page 208: 12


The function will behave like $3x^4$.

Work Step by Step

Consider the graph: $f(x)=3x^4−x^3+5x^2−2x−7$ When considering behavior at infinity, we look at the highest degree of $x$ in the function. At infinity, the lower degrees of $x$ will be negligible comp,ared to the larger degrees of x. We see that the term with the highest degree is $3x^4$. This means that the function will behave like $3x^4$.
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