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: 34

Answer

(a) See graph. (b) $(-\infty,0)U(0,\infty)$, $(3,\infty)$ (c) $x=0$, $y=3$

Work Step by Step

(a) To obtain the graph of $F(x)=3+\frac{1}{x^2}$ from $y=\frac{1}{x^2}$, shift the curve 3 units up. See graph. (b) Based on the graph, we can find the domain as $(-\infty,0)U(0,\infty)$ and range as $(3,\infty)$ (c) We can identify the vertical asymptote $x=0$, horizontal asymptote $y=3$, or oblique asymptote $none$.
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