Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 3 - Section 3.2 - Polynomial Functions and Their Graphs - 3.2 Exercises - Page 266: 10

Answer

graph I

Work Step by Step

As $x\rightarrow-\infty,$ $x^{2} $ is a large positive number, and so is $(x^{2}-4)$ Their product is positive. The minus sign changes it to negative So as $ x\rightarrow-\infty$, Q(x)$\rightarrow-\infty$ (the graph sinks down on the far left) As $x\rightarrow+\infty,$ $x^{2} $ is a large positive number, and so is $(x^{2}-4)$ Their product is positive. The minus sign changes it to negative So as $ x\rightarrow$+$\infty$, Q(x)$\rightarrow-\infty$ (the graph sinks down on the far right) The graph that fits this behavior is graph I
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