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.
