#### Answer

See the graph below:

#### Work Step by Step

Convert the function into the form: $\text{Quotient}+\frac{\text{Remainder}}{\text{Divisor}}$.
$\begin{align}
& g\left( x \right)=\frac{2x+7}{x+3} \\
& =2+\frac{1}{x+3}
\end{align}$
Where the quotient is $2$ , the remainder is $1,$ and the divisor is $x+3$.
The rational root is
$\begin{align}
& x+3=0 \\
& x=-3
\end{align}$
The graph has a vertical asymptote along $x=-3$. The graph has a horizontal asymptote along $y=2$.