Answer
See below:
Work Step by Step
The function is,
$f\left( x \right)=\frac{4x-4}{x-2}$,
Replace x as $-x$ to check the symmetry.
$\begin{align}
& f\left( -x \right)=\frac{4\left( -x \right)-4}{-x-2} \\
& =\frac{-\left( 4x+4 \right)}{-\left( x+2 \right)} \\
& =\frac{4x+4}{x+2}
\end{align}$
Since $f\left( x \right)\ne f\left( -x \right)$, therefore graph is not in symmetry to the y-axis.
Now put $x=0$ and get the y-intercept.
$\begin{align}
& f\left( x \right)=\frac{4x-4}{x-2} \\
& =\frac{4\times 0-4}{0-2} \\
& =\frac{-4}{-2} \\
& =2
\end{align}$
Thus, the graph of the function passes through the point $\left( 0,2 \right)$.
Substitute $0$ for $f\left( x \right)$ to get $x-\text{intercept}$.
$\begin{align}
& 4x-4=0 \\
& 4x=4 \\
& x=1
\end{align}$
Hence the graph passes through the point $\left( 1,0 \right)$
For the vertical asymptotes the denominator is equal to zero, so to find out the vertical asymptotes,
$\begin{align}
& x-2=0 \\
& x=2
\end{align}$
The vertical asymptote $x=2$.
Take the ratio of the coefficient of x in the numerator and denominator to get the horizontal asymptotes.
$\begin{align}
& y=\frac{4}{1} \\
& =4
\end{align}$
Collect all the points of the vertical asymptotes(x) and horizontal asymptotes(y).
