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.
-$$y = 0.58 x ^ { 4 } + x ^ { 2 } - 4$$
A) $\mathrm { y }$-axis only
B) $x$-axis only
C) origin only
D) none of these

Question

Quizplus · Accepted Answer

The given equation is even, meaning all the powers of $x$ are even ($x^4$ and $x^2$), which makes the graph symmetric with respect to the $y$-axis. There's no indication of symmetry with respect to the $x$-axis or the origin.

Determine Whether the Equation Has a Graph That Is Symmetric y=0.58x4+x2−4y = 0.58 x ^ { 4 } + x ^ { 2 } - 4y=0.58x4+x2−4

Determine Whether the Equation Has a Graph That Is Symmetric $y = 0.58 x ^ { 4 } + x ^ { 2 } - 4$