#### Answer

Shown below is the final graph:

#### Work Step by Step

Consider the function $g\left( x \right)=\frac{2x-9}{x-4}$
Convert the function into the form: $\text{Quotient}+\frac{\text{Remainder}}{\text{Divisor}}$.
$\begin{align}
& g\left( x \right)=\frac{2x-9}{x-4} \\
& g\left( x \right)=2+\frac{\left( -1 \right)}{x-4}
\end{align}$
Where quotient is $2$ , remainder is $-1,$ and divisor is $x-4$.
The rational root is
$\begin{align}
& x-4=0 \\
& x=4
\end{align}$
The graph of the function $f\left( x \right)=-\frac{1}{x}$ is the mirror image of the function $f$ with respect to the x-axis.
When x is changed to x-a, this implies that the graph of the function is shifted by a units to the left.
Shift the graph to the right by 4 units: $f\left( x \right)=\frac{-1}{x-4}$.
Now, shift the graph upwards by 2 units.
The graph has a vertical asymptote along $x=4$. The graph has a horizontal asymptote along $y=2$.