Calculus 10th Edition

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.