Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 4 - Polynomial and Rational Functions - 4.2 Properties of Rational Functions - 4.2 Assess Your Understanding - Page 197: 43

Answer

(a) See graph. (b) $(-\infty,0)U(0,\infty)$, $(-\infty,1)$ (c) $x=0$, $y=1$

Work Step by Step

(a) To obtain the graph of $R(x)=\frac{x^2-4}{x^2}=1-\frac{4}{x^2}$ from $y=\frac{1}{x^2}$, stretch the curve vertically by a factor of 4, reflect across the x-axis, then shift 1 unit up. See graph. (b) Based on the graph, we can find the domain as $(-\infty,0)U(0,\infty)$ and range as $(-\infty,1)$ (c) We can identify the vertical asymptote $x=0$, horizontal asymptote $y=1$, or oblique asymptote $none$.
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