Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.3 - More on Functions and Their Graphs - Concept and Vocabulary Check - Page 194: 3


The graph of an equation is symmetric with respect to the y-axis if substituting \[-x\text{ for }x\] in the equation results in an equivalent equation.

Work Step by Step

We know that if the graph of a function is symmetric about y-axis, then it is an even function and if replacement of $x$ by $-x$, there will be no effect on the function. For example, \[y={{x}^{2}}+2\] Replace $x$ by $-x$: \[\begin{align} & y={{\left( -x \right)}^{2}}+2 \\ & y={{x}^{2}}+2 \\ \end{align}\] Thus, this equation is an equivalent equation. So, the graph will be symmetric with respect to the y-axis.
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