Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin.
-$$y = - 2 x ^ { 3 } + 5 x$$
A) x-axis
B) y-axis
C) origin
D) x-axis, y-axis, origin
E) none

Question

Quizplus · Accepted Answer

A graph is symmetric with respect to the origin if replacing $x$ with $-x$ and $y$ with $-y$ results in the original equation. For the given equation $y = -2x^3 + 5x$, replacing $x$ with $-x$ gives $-y = -2(-x)^3 + 5(-x)$ or $-y = -2x^3 + 5x$, which is equivalent to the original equation when $y$ is replaced with $-y$. This shows symmetry with respect to the origin.

Determine Whether the Graph of the Equation Is Symmetric with Respect