Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin.
-$y = - 5 x ^ { 3 }$
A) x -axis
B) Origin
C) No symmetry
D) y -axis

Question

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin.
-$y = - 5 x ^ { 3 }$
A)  x -axis
B) Origin
C) No symmetry
D)  y -axis

Quizplus · Accepted Answer

The graph of $y = -5x^3$ is symmetric with respect to the origin because replacing $x$ with $-x$ and $y$ with $-y$ results in the original equation: $-y = -5(-x)^3$, which simplifies back to $y = -5x^3$. This indicates origin symmetry.

Determine Whether the Graph of the Given Equation Is Symmetric y=−5x3y = - 5 x ^ { 3 }y=−5x3

Determine Whether the Graph of the Given Equation Is Symmetric $y = - 5 x ^ { 3 }$