College Algebra (10th Edition)

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

Chapter 3 - Section 3.3 - Properties of Function - 3.3 Assess Your Understanding: 3

Answer

The given equation is symmetric with respect to the y-axis.

Work Step by Step

$\bf\text{Test for Symmetry with x-axis}$: Replace $y$ with $-y$ to obtain: $y=5x^2-1 \\-y=5x^2-1 \\-1(-y)=-1(5x^2-1) \\y=-5x^2+1$ The resulting equation is different from the original equation. Thus, the given equation is not symmetric with respect to the x-axis. $\bf\text{Test for Symmetry with y-axis}$: Replace $x$ with $-x$ to obtain: $y=5x^2-1 \\y=5(-x)^2-1 \\y=5x^2-1$ The resulting equation is the same as the original equation. Thus, the given equation is symmetric with respect to the y-axis. $\bf\text{Test for Symmetry with the Origin}$: Replace $x$ with $-x$ and $y$ with $-y$ to obtain: $y=5x^2-1 \\-y=5(-x)^2-1 \\-y=5x^2-1 \\-1(-y)=-1(5x^2-1) \\y=-5x^2+1 $ The resulting equation is different from the original equation. Thus, the given equation is not symmetric with respect to the origin.
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