Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter P - P.1 - Graphs and Models - Exercises: 29

Answer

Symmetric to only x-axis

Work Step by Step

Substitute -x for x. If equation is equivalent, graph is symmetric to y-axis. $y^{2}$=$(-x)^{3}$-8(-x) $y^{2}$=$-x^{3}$+8x Equations are not equivalent, so not symmetric to y-axis. Substitute -y for y. If equation is equivalent, graph is symmetric to x-axis. $(-y)^{2}$=$x^{3}$-8x $y^{2}$=$x^{3}$-8x Equivalent to initial equation, so symmetric with x-axis. Substitute -y for y and -x for x. If equation is equivalent, graph is symmetric to origin. $(-y)^{2}$=$(-x)^{3}$-8(-x) $y^{2}$=$-x^{3}$+8x Equations are not equivalent, so not symmetric to origin.
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