Answer
Symmetric to origin only
Work Step by Step
Substitute -x for x. If equation is equivalent, graph is symmetric to y-axis.
y=$(-x)^{3}$+(-x)
y=$-x^{3}$-x
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=$x^{3}$+x
y=$-x^{3}$-x
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.
-y=$(-x)^{3}$+(-x)
y=$x^{3}$+x
Equations are equivalent, so symmetric to origin.
