Answer
The graph is shown below:
Work Step by Step
Step 1: Substitute $x=-x$
$\begin{align}
& f\left( x \right)=\frac{4x}{x-2} \\
& f\left( -x \right)=\frac{4\left( -x \right)}{\left( -x \right)-2} \\
& =\frac{-4x}{-\left( x+2 \right)} \\
& =\frac{4x}{x+2}
\end{align}$
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.
Step 2: To calculate the x intercepts equate $f\left( x \right)=0$.
$\begin{align}
& \frac{4x}{x-2}=0 \\
& x=0
\end{align}$
Step 3: To calculate the y intercepts evaluate $f\left( 0 \right)$
$\begin{align}
& f\left( 0 \right)=\frac{4\left( 0 \right)}{\left( 0 \right)-2} \\
& f\left( 0 \right)=0 \\
\end{align}$
Step 4: Since the degree of the numerator is equal to the denominator, the horizontal asymptote is:
$y=2$.
Step 5: For the vertical asymptote, equate the denominator to 0.
$\begin{align}
& x-1=0 \\
& x=1
\end{align}$
