College Algebra (10th Edition)

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

Chapter 2 - Review Exercises - Page 195: 9

Answer

The x-intercepts are (-1,0), (0,0), and (1,0) The y-intercept is (0,0) The equation has symmetry only with respect to the origin.

Work Step by Step

To find the x-intercept(s), we set y to 0 and solve for x: $0=x^3-x$ $0=x(x^2-1)$ $x_1=0$ $0=(x_2)^2-1\rightarrow \sqrt{(x_2)^2}=\sqrt1 \rightarrow x_2=\pm1$ To find the y-intercept(s), we set x to y and solve for y: $y=0^3-0$ $y=0$ To test for symmetry with respect to the x-axis, we substitute y for -y and check if it equals the original equation: $(-y)=x^3-x$ $-y=x^3-x$ nope To test for symmetry with respect to the y-axis, we substitute x for -x and check if it equals the original equation: $y=(-x)^3-(-x)$ $y=-x^3+x$ nope 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: $(-y)=(-x)^3-(-x)$ $-y=-(x^3-x)$ $y=x^3-x\checkmark$
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