Question 107633
The vertical asymptote occurs when the denominator goes to zero, that is, 
f(x) goes to {{{infinity}}} and {{{-infinity}}}.
{{{x+2=0}}}
{{{x=-2}}}
The horizontal asymptotes occur as x goes to {{{infinity}}} and {{{-infinity}}}.
{{{f(x)=(2x+3)/(x+2)}}}
As x goes to {{{infinity}}},
f(x) looks like {{{2x/x}}} or 2. 
As x goes to {{{-infinity}}},
f(x) looks like {{{2(-x)/(-x)}}} or 2.
The horizontal asymptote is y=2. 
{{{ graph( 300, 300, -5, 5, -10, 10, (2x+3)/(x+2),2) }}}