University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 1 - Section 1.1 - Functions and Their Graphs - Exercises - Page 12: 17

Answer

$\mathrm{Domain:}\ \ (-\infty,\infty)$ $\mathrm{See\:the\:graph\:below.}$

Work Step by Step

We can take the square root only of positive numbers. Since the absolute value of $\ x\ $ will always give positive numbers, the domain of the given function is $\ y=\sqrt{|x|}\ $ is $\ (-\infty,\infty).$ The graph of the given function $\ y=\sqrt{|x|}\ $ is similar to the graph of $\ y=\sqrt{x}\ $ when $\ x\geq0\ $, but reflects itself along the $\ \mathrm{y-axis}\ $ when $\ x<0.$ See the graph below.
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