Answer
See below:
Work Step by Step
Consider the function $g\left( x \right)=\frac{3x+7}{x+2}$ and convert into the form: $\text{Quotient}+\frac{\text{Remainder}}{\text{Divisor}}$.
$\begin{align}
& g\left( x \right)=\frac{3x-7}{x-2} \\
& g\left( x \right)=3+\frac{\left( -1 \right)}{x-2}
\end{align}$
where quotient is $3$ , remainder is $-1,$ and divisor is $x-2$.
The rational root is
$\begin{align}
& x-2=0 \\
& x=2
\end{align}$
The graph of the function $f\left( x \right)=-\frac{1}{x}$ is the mirror image of the function $f$ about 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 right.
The graph is shifted to the right by 2 units:
$f\left( x \right)=\frac{-1}{x-2}$.
Now, shift the graph 3 units upward $\frac{-1}{x-2}$, to give the final graph.
The graph has a vertical asymptote along $x=2$. The graph has a horizontal asymptote along $y=3$
