Answer
Refer to the graph below.
Work Step by Step
The $x$-intercepts of the function's graph can be found by equating each factor to zero then solving each equation to obtain:
\begin{align*}
x-3&=0 &\text{or}& &x+2=0& &\text{or}& &3x-2=0\\
x&=3 &\text{or}& &x=-2& &\text{or}& &3x=2\\
x&=3 &\text{or}& &x=-2& &\text{or}& &x=\frac{2}{3}\\
\end{align*}
Thus, the $x$-intercepts are $-2, \frac{2}{3},$ and $3$.
The $y$_intercept of the function can be found by setting $x=0$ then solving for $y$:
\begin{align*}
P(0)&=(0-3)(0+2)(3\cdot0-2)\\
P(0)&=-3(2)(-2)\\
P(0)&=12
\end{align*}
Thus, the $y$-intercept is $12$
Create a table of values to obtain the one below.
Then, plot each ordered pair and connect the points using a smooth curve.
Refer to the graph above.
