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 F - Foundations: A Prelude to Functions - Section F.2 Graphs of Equations in Two Variables; Intercepts; Symmetry - F.2 Assess Your Understanding - Page 17: 53


Intercepts are$ y =-2, y =2, x =-4$; The graph is symmetric about the x-axis.

Work Step by Step

To find the x-intercept of an equation, you set y = 0 and solve, and to find the y-intercept of an equation, you must set x = 0 and solve. To find the y-intercepts, we use the expression $y^{2} = 4$. Taking the square root of both sides, $y = 2$ or $y = -2$. To find the x-intercepts, we use the expression $0 = x + 4$, and therefore, $x = -4$. To check for symmetry about the x-axis, replace every instance of y with -y in the original equation. The new equation must be equivalent to the original. Since $(-y)^{2} = x +4$ is the same as $y^{2} = x+4$, there is symmetry about the x-axis. For symmetry about the y-axis, replace every instance of x with -x. Since $y^{2} = x+4$ is not the same as $y^{2} = -x+4$, there is no symmetry about the y-axis.
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