Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 3 - Section 3.6 - Rational Functions - 3.6 Exercises - Page 308: 13

Answer

Domain: (-∞, 1) U (1, ∞) Range: (-∞, 0) U (0, ∞) See graph below, green graph is the answer.

Work Step by Step

The question asks for a graph of the function and the function's domain and range. Given $r(x) = \frac{1}{x-1}$ From $\frac{1}{x}$, the graph is transformed one unit to the right The vertical asymptote is at x= 1, so the domain is (-∞, 1) U (1, ∞) The horizontal asymptote is at y = 0, so the range is (-∞, 0) U (0, ∞) Blue graph is $\frac {1}{x}$ Green graph is $r(x) = \frac{1}{x-1}$
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