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.
-$$y = - 7 x ^ { 3 } + 9 x$$
A) $x$-axis only
B) $\mathrm { y }$-axis only
C) origin only
D) $x$-axis, $y$-axis, origin

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 $y = -7x^3 + 9x$, replacing $x$ with $-x$ gives $y = -7(-x)^3 + 9(-x) = -(-7x^3 + 9x) = 7x^3 - 9x$, which is the original equation negated, indicating symmetry with respect to the origin.

Determine Whether the Equation Has a Graph That Is Symmetric y=−7x3+9xy = - 7 x ^ { 3 } + 9 xy=−7x3+9x

Determine Whether the Equation Has a Graph That Is Symmetric $y = - 7 x ^ { 3 } + 9 x$