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: 58

Answer

(a) See graph (red). (b) domain $\{x|x\ne-2\}$, range $\{y|y\gt-1\}$. (c) vertical asymptote $x=-2$, horizontal asymptote $y=-1$.

Work Step by Step

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