Answer
No symmetry
Work Step by Step
Testing symmetry with respect to $x$-axis:
$$-y=x^4+x^3-1$$ $$y=-x^4-x^3+1$$
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:
$$y=(-x)^4+(-x)^3-1$$ $$y=x^4-x^3-1$$
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:
$$-y=(-x)^4+(-x)^3-1$$ $$-y=x^4-x^3-1$$ $$y=-x^4+x^3+1$$
Since the resulting equation is not the same as the original equation, the equation is not symmetric with respect to origin.
The sketch of the graph is as shown.
