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.
-$$y = 5 x ^ { 5 } - 3 x ^ { 3 }$$
A) none of these
B) origin only
C) $y$-axis 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 $y = 5x^5 - 3x^3$, replacing $x$ with $-x$ gives $y = -5x^5 + 3x^3$, which is the original equation negated ($-y$). This indicates symmetry with respect to the origin.

Determine Whether the Equation Has a Graph That Is Symmetric y=5x5−3x3y = 5 x ^ { 5 } - 3 x ^ { 3 }y=5x5−3x3

Determine Whether the Equation Has a Graph That Is Symmetric $y = 5 x ^ { 5 } - 3 x ^ { 3 }$