College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 3 - Section 3.4 - Library of Functions; Piecewise-defined Function - 3.4 Assess Your Understanding - Page 244: 9



Work Step by Step

We know that $y=|x|$ is symmetric about the y-axis because it has the form: $f(x)=\left\{\begin{array}{ll} -x & x\lt0 \\ x & x\gt0 \end{array}\right.$ That is, the graph is that of a line with slope -1 until $x=0$, followed by a line with slope $1$ after $x=0$ and both lines have the same $y-intercept$ of $0$. Hence, the graph is symmetrical.
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