Answer
The graph of the function is:
Work Step by Step
Substitute $x=-x$.
$\begin{align}
& f\left( x \right)=\frac{3x}{x-1} \\
& f\left( -x \right)=\frac{3\left( -x \right)}{\left( -x \right)-1} \\
& =\frac{-3x}{-\left( x+1 \right)} \\
& =\frac{3x}{x+1}
\end{align}$
Therefore, the function $f\left( -x \right)$ is not equal to either $f\left( x \right)$ or $-f\left( x \right)$. Hence, the graph of the function is symmetric neither about the $y$ -axis nor about the origin.
To calculate the x intercepts equate $f\left( x \right)=0$.
$\begin{align}
& \frac{3x}{x-1}=0 \\
& x=0
\end{align}$
