Determine whether the equation has a graph that is symmetric with respect to the y-axis, the x-axis, the origin, or none of
these.
-$$y = - 6 x ^ { 3 } + 2 x$$
A) origin only
B) $y$-axis only
C) $x$-axis, $y$-axis, origin
D) $x$-axis only

Question

Quizplus · Accepted Answer

The given equation $y = -6x^3 + 2x$ is symmetric with respect to the origin because replacing $x$ with $-x$ results in $y = -6(-x)^3 + 2(-x) = -y$, which satisfies the condition for origin symmetry.

Determine Whether the Equation Has a Graph That Is Symmetric y=−6x3+2xy = - 6 x ^ { 3 } + 2 xy=−6x3+2x

Determine Whether the Equation Has a Graph That Is Symmetric $y = - 6 x ^ { 3 } + 2 x$