#### Answer

Thus, $x=0$ is the only x-intercept.
Thus, $y=0$ is the only y-intercept.
Origin symmetry.

#### Work Step by Step

To find the x-intercept of an equation, we set $y=0$ and solve:
$y=\sqrt[3]{x}$
$0=\sqrt[3]{x}$
$x=0^3=0$
Thus, $x=0$ is the only x-intercept.
Similarly, to find the y-intercept of an equation, we set $x=0$ and solve:
$y=\sqrt[3]{x}$
$y=\sqrt[3]{0}=0$
Thus, $y=0$ is the only y-intercept.
To check for symmetry about the x-axis, we replace every instance of $y$ with $-y$ in the original equation. The new equation must be equivalent to the original.
We have:
$-y= \sqrt[3]{x}$
which is not the same as $y= \sqrt[3]{x}$
Thus, there is no symmetry about the x-axis.
For symmetry about the y-axis, replace every instance of $x$ with $-x$. We have
$y = \sqrt[3]{-x}=-\sqrt[3]{x}$
which is not the same as $y = \sqrt[3]{x}$
Thus, there is no symmetry about the y-axis.
However, the graph is symmetric with respect to the origin since if we replace $x,y$ by $-x,-y$, we get the same equation:
$-y= \sqrt[3]{-x}= -\sqrt[3]{x}$
Thus
$y= \sqrt[3]{x}$.
which is the same as the original equation. Thus, we have origin symmetry.