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 1 - Functions and Their Graphs - Section 1.4 Library of Functions; Piecewise-defined Functions - 1.4 Assess Your Understanding - Page 86: 36

Answer

(a) $\{x|x=all\ real\ numbers\}$. (b) $(0,0)$. (c) See graph. (d) $\{y|y=all\ real\ numbers\}$ (e) not continuous

Work Step by Step

(a) Based on the given piece-wise function, we can find the domain as $\{x|x=all\ real\ numbers\}$. (b) We can locate the x-intercept(s) (let y=0) as $(0,0)$, y-intercept(s) (let x=0) as $(0,0)$. (c) See graph. (d) Based on the graph, we can find the range as $\{y|y=all\ real\ numbers\}$ (e) We can see that $f$ is not continuous on its domain (break at $x=0$).
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