Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither.
-$$f ( x ) = x ^ { 3 } - 4 x$$
A) origin symmetry
B) y-axis symmetry
C) neither

Question

Quizplus · Accepted Answer

A function has origin symmetry if $f(-x) = -f(x)$. For the given polynomial $f(x) = x^3 - 4x$, if we substitute $-x$ for $x$, we get $f(-x) = (-x)^3 - 4(-x) = -x^3 + 4x = -(x^3 - 4x) = -f(x)$, which confirms the function has origin symmetry.

Determine Whether the Graph of the Polynomial Has Y-Axis Symmetry f(x)=x3−4xf ( x ) = x ^ { 3 } - 4 xf(x)=x3−4x

Determine Whether the Graph of the Polynomial Has Y-Axis Symmetry $f ( x ) = x ^ { 3 } - 4 x$