Answer
There is no symmetry about x-axis, about y-axis nor about the origin.
See graph
The intercepts: $(1,0)$, $(0,-1)$.
Work Step by Step
$$y=x^3-1$$
Testing for symmetry about the x-axis:
$$-y=x^3-1$$ $$y=-x^3+1$$
Since the resulting equation is not the same as the original equation, there is no symmetry about the x-axis.
Testing for symmetry about the y-axis:
$$y=(-x)^3-1$$ $$y=-x^3-1$$
Since the resulting equation is not the same as the original equation, there is no symmetry about the y-axis.
Testing for symmetry about the origin:
$$-y=(-x)^3-1$$ $$-y=-x^3-1$$ $$y=x^3+1$$
Since the resulting equation is not the same as the original equation, there is no symmetry about the origin.
Finding x-intercept where $y=0$:
$$0=x^3-1$$ $$x^3=1$$ $$x=1$$
Thus, a point is at $(1,0)$.
Finding y-intercept where $x=0$:
$$y=0^3-1$$ $$y=-1$$
Thus, another point is at $(0,-1)$.
At $x=-1$:
$$y=(-1)^3-1=-2$$
Thus, another point is $(-1,-2)$
Using the points, the graph is as shown below.
The intercepts are for x-intercept is $(1,0)$ and for y-intercept is $(0,-1)$.
