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 18: 82

Answer

(a) $(\pm4,0)$, $(0,\pm4)$, (b) symmetric with respect to the x-axis, y-axis, and the origin. (c) See graph.

Work Step by Step

(a) Given $x^2+y^2=16$, we can find the x-intercept(s) (let y=0) as $(\pm4,0)$, y-intercept(s) (let x=0) as $(0,\pm4)$, (b) To test symmetry, replace $(x,y)$ with $(x,-y)$ (x-axis symmetry), or $(-x,y)$ (y-axis symmetry), or $(-x,-y)$ (origin symmetry), and we can find the equation is symmetric with respect to the x-axis, y-axis, and the origin. (c) See graph.
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