College Algebra (10th Edition)

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

Chapter 2 - Test - Page 196: 6

Answer

The x-intercepts are (-3,0) and (3,0) The y-intercept is (0,9) The equation has symmetry only with respect to the y-axis.

Work Step by Step

To find the x-intercept(s), we set y to 0 and solve for x: $x^2+0=9$ $x^2=9$ $\sqrt{x^2}=\sqrt9$ $x=\pm3$ To find the y-intercept(s), we set x to y and solve for y: $0^2+y=9$ $y=9$ To test for symmetry with respect to the x-axis, we substitute y for -y and check if it equals the original equation: $x^2+(-y)=9$ $x^2-y=9$ nope To test for symmetry with respect to the y-axis, we substitute x for -x and check if it equals the original equation: $(-x)^2+y=9$ $x^2+y=9\checkmark$ To test for symmetry with respect to the origin, we substitute x for -x, substitute y for -y and check if it equals the original equation: $(-x)^2+(-y)=9$ $x^2-y=9$ nope
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