## Calculus 10th Edition

Published by Brooks Cole

# Chapter P - P.1 - Graphs and Models - Exercises: 47

#### Answer

Symmetric to origin x and y-intercept at (0,0)

#### Work Step by Step

Find Intercepts: x-int x=$0^{3}$ x=0 x-intercept at (0,0) y-int 0=$y^{3}$ y=0 y-intercept at (0,0) Find Symmetry: Substitute -x for x. If equation is equivalent, graph is symmetric to y-axis. -x=$y^{3}$ x=-$y^{3}$ Equations are not equivalent, so not symmetric to y-axis. Substitute -y for y. If equation is equivalent, graph is symmetric to x-axis. x=$(-y)^{3}$ x=-$y^{3}$ Equations are not equivalent, so not symmetric to x-axis. Substitute -y for y and -x for x. If equation is equivalent, graph is symmetric to origin. (-x)=$(-y)^{3}$ x=$y^{3}$ Equations are equivalent, so function is symmetric to origin.

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