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: 66

Answer

$ (\pm2,0)$, symmetric with respect to the origin.

Work Step by Step

Step 1. For x-intercept(s), let $y=0$, we have $x^2=4\longrightarrow (\pm2,0)$, no y-intercept(s) as we can not let $x=0$, Step 2. To test for x-axis symmetry, replace $(x,y)$ with $(x,-y)$, we have $-y=\frac{(x)^2-4}{2(x)}$ which is different from the original equation, thus it is not symmetric with respect to the x-axis, Step 3. To test for y-axis symmetry, replace $(x,y)$ with $(-x,y)$, we have $y=\frac{(-x)^2-4}{2(-x)}$ which is different from the original equation, thus it is not symmetric with respect to the y-axis, Step 4. To test for origin symmetry, replace $(x,y)$ with $(-x,-y)$, we have $-y=\frac{(-x)^2-4}{2(-x)}$ which is the same as the original equation, thus it is symmetric with respect to the origin.
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