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.
-$y = 0.11 x ^ { 4 } + x ^ { 2 } + 6$
A) origin only
B) none of these
C) $y$-axis only
D) x-axis only

Question

Quizplus · Accepted Answer

A graph is symmetric with respect to the y-axis if, for every point (x, y) on the graph, the point (-x, y) is also on the graph. The given equation $y = 0.11x^4 + x^2 + 6$ satisfies this condition because when x is replaced with -x, the equation remains unchanged due to the even powers of x. This means the graph is symmetric with respect to the y-axis.

Determine Whether the Equation Has a Graph That Is Symmetric y=0.11x4+x2+6y = 0.11 x ^ { 4 } + x ^ { 2 } + 6y=0.11x4+x2+6

Determine Whether the Equation Has a Graph That Is Symmetric $y = 0.11 x ^ { 4 } + x ^ { 2 } + 6$