   Chapter P.1, Problem 31E

Chapter
Section
Textbook Problem

Testing for Symmetry In Exercises 29-40, test for symmetry with respect to each axis and to the origin. y 2 = x 3 − 8 x

To determine

To calculate: The equation y² = x³8x for symmetry with respect to each axis and the origin.

Explanation

Given: y² = x³8x

Calculation:

Replacing x by –-x in the given equation must yield an equivalent equation for the graph to be symmetric with respect to y-axis. The equation that we obtain is

y² = (x)³8(x)y² = x³+8x

Replacing y by –-y in the given equation must yield an equivalent equation for the graph to be symmetric with respect to x-axis. The equation that we obtain is

(y)² = x³<

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