Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin.
-$$y = \frac { 4 x } { x ^ { 2 } + 16 }$$
A) y-axis
B) x-axis
C) origin
D) x-axis, y-axis, origin
E) none

Question

Quizplus · Accepted Answer

The graph is symmetric with respect to the origin because replacing $x$ with $-x$ and $y$ with $-y$ results in the same equation: $-y = \frac{4(-x)}{(-x)^2 + 16} = \frac{-4x}{x^2 + 16}$, which simplifies to $y = \frac{4x}{x^2 + 16}$.

Determine Whether the Graph of the Equation Is Symmetric with Respect