Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 4 - 4.1 - Rational Functions and Asymptotes - 4.1 Exercises - Page 315: 21


Domain: $x \ne \pm4$ Vertical asymptotes: $x=-4$ Horizontal asymptotes: $y=0$

Work Step by Step

Find the domain: $x^2 -16 \ne 0$ $x^2\ne16$ $x \ne\pm 4$ Identify vertical asymptotes: $\frac{x-4}{x^2-16}=\frac{x-4}{(x-4)(x+4)}=\frac{1}{x+4}$ $x=-4$ Identify horizontal asymptotes: $f(x) \rightarrow$ as $x\rightarrow \infty$ $y=0$
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