Answer
Graph:
Work Step by Step
The degree of the numerator is 1, which is equal to the degree of the denominator, so we can write
$y=f(x)=\displaystyle \frac{x+2+1}{x+2}=1+\frac{1}{x+2}$
$\displaystyle \lim_{x\rightarrow+\infty}f(x)=1, \quad \lim_{x\rightarrow-\infty}f(x)=1,$
so, the horizontal asymptote is $y=1.$
f(x) is not defined for $x=-2$. Vertical asymptote : $x=-2$, with
$\displaystyle \lim_{x\rightarrow-2^{-}}f(x)=-\infty, \quad \displaystyle \lim_{x\rightarrow-2^{+}}f(x)=+\infty$
Plot some points:
y-intercept: $f(0)=1.5,$ plot ($0,1.5)$.
Also, use
$f(-1)=2$ to plot $(-1,2).$
$f(-3)=0$ to plot $(-3,0).$
Graph the asymptotes, and use the behavior in the vicinity of the asymptotes to sketch the graph.