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.
-$$y = - 6 x ^ { 4 } - 5 x + 5$$
A) $x$-axis only
B) none of these
C) origin only
D) y-axis only

Question

Quizplus · Accepted Answer

The given equation $y = -6x^4 - 5x + 5$ is not symmetric with respect to the x-axis, y-axis, or the origin. For symmetry about the y-axis, replacing $x$ with $-x$ should yield the same equation, which does not happen here due to the $-5x$ term. For symmetry about the x-axis, replacing $y$ with $-y$ should yield the same equation, which is not the case. For symmetry about the origin, replacing both $x$ with $-x$ and $y$ with $-y$ should yield the original equation, which also does not happen due to the $-5x$ term.

Determine Whether the Equation Has a Graph That Is Symmetric y=−6x4−5x+5y = - 6 x ^ { 4 } - 5 x + 5y=−6x4−5x+5

Determine Whether the Equation Has a Graph That Is Symmetric $y = - 6 x ^ { 4 } - 5 x + 5$