Answer
For $y = -4x^3 + x$, it has a graph that is symmetric with respect to the origin.
Work Step by Step
In $y = -4x^3 + x$,
a) To test for symmetry w.r.t the $x$-axis
replace $y$ with $-y$, we have
$(-y) = -4x^3 + x$
$-y = -4x^3 + x$
$y = 4x^3 - x$
which the result is not the same as the original equation, therefore, it is not symmetric with respect to the $x$-axis
b) To test for symmetry w.r.t the $y$-axis
replace $x$ with $-x$, we have
$y = -4(-x)^3 + (-x)$
$y = 4x^3 - x$
which the result is not the same as the original equation, therefore, it is not symmetric with respect to the $y$-axis
c) To test for symmetry w.r.t the origin
replace $x$ with $-x$ and $y$ with $-y$, we have
$(-y) = -4(-x)^3 + (-x)$
$-y = 4x^3 - x$
$y = -4x^3 + x$
which the result is the same as the original equation, therefore, it is symmetric with respect to the origin
