Answer
The graph of the function $g\left( x \right)=\frac{1}{x+2}+3:$
Work Step by Step
Convert the function into the form: $\text{quotient}+\frac{\text{remainder}}{\text{divisor}}$.
$\begin{align}
& g\left( x \right)=\frac{3x+7}{x+2} \\
& g\left( x \right)=3+\frac{1}{x+2}
\end{align}$
Where quotient is $3$ , remainder is $1,$ and divisor is $x+2$.
The rational root is
$\begin{align}
& x+2=0 \\
& x=-2
\end{align}$
When x is changed to $x+a$, this implies that the graph of the function is shifted by a units to the left.The graph of the function $f\left( x \right)=\frac{1}{x+2}$ is shifted left by 2 units.
The graph has a vertical asymptote along $x=-2$. The graph has a horizontal asymptote along $y=3$.
