Answer
Symmetry with respect to the origin
Work Step by Step
Testing symmetry with respect to $x$-axis:
$$-y=3x^3$$ $$y=-3x^3$$
Since the resulting equation is not the same as the original equation, the equation is not symmetric with respect to $x$-axis.
Testing symmetry with respect to $y$-axis:
$$y=3(-x)^3$$ $$y=-3x^3$$
Since the resulting equation is not the same as the original equation, the equation is not symmetric with respect to $y$-axis.
Testing symmetry with respect to origin:
$$-y=3(-x)^3$$ $$-y=-3x^3$$ $$y=3x^3$$
Since the resulting equation is the same as the original equation, the equation is symmetric with respect to origin.
The sketch of the graph is as shown.
