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 3.4 Properties of Rational Functions - 3.4 Assess Your Understanding - Page 241: 60

Answer

(a) See graph (red). (b) domain $\{x|x\ne-3\}$, range $\{y|y\lt2\}$. (c) vertical asymptote $x=-3$, horizontal asymptote $y=2$.

Work Step by Step

(a) To obtain the graph of $y=2-\frac{2}{x^2+6x+9}=2-\frac{2}{(x+3)^2}$ from $y=\frac{1}{x^2}$, shift the curve 3 unit(s) to the left, stretch vertically by a factor of 2, reflect across the x-axis, then shift 2 units up. See graph (red). (b) We can find the domain $\{x|x\ne-3\}$, range $\{y|y\lt2\}$. (c) We can identify the vertical asymptote $x=-3$, horizontal asymptote $y=2$.
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