Answer
The graph is shown below:
Work Step by Step
To find the x-intercepts of the function equate the function ${{x}^{2}}\left( x-3 \right)$ to zero.
$\begin{align}
& {{x}^{2}}\left( x-3 \right)=0 \\
& x=0,3
\end{align}$
Thus, $x=0$ and $x=3$ are the x-intercepts of the function.
To find the y-intercept of the function, find the value of $f\left( 0 \right)$.
$\begin{align}
& f\left( 0 \right)={{0}^{2}}\left( 0-3 \right) \\
& =0
\end{align}$
Thus, the y-intercept is 0.
Substitute x with $-x$ to check the symmetry of the function:
$\begin{align}
& f\left( -x \right)={{\left( -x \right)}^{2}}\left( -x-3 \right) \\
& =-{{x}^{2}}\left( x+3 \right)
\end{align}$
Since $f\left( x \right)\ne f\left( -x \right)$, the graph is not symmetric with respect to the y-axis and since $f\left( -x \right)\ne -f\left( x \right)$, thus, the graph is not symmetric through the origin.
