Question 971228
A matter of polynomial division; the quotient is the slant asymptote and the remainder will tend toward 0 as x goes to the left or right unbounded.



Choosing synthetic division,


_________3_________|_________1________1________-2
___________________|
___________________|_________________3________12
___________________________________________________
____________________________1________4________10


Remainder is 10; which would represent {{{10/(x-3)}}}.
The slant asymptote is {{{highlight(y=x+4)}}}.


y-intercept?  Let x=0 and evaluate f.


x-intercepts?   Check for roots of the numerator.
Discriminant, {{{1-4(-2)=9}}};
{{{x=(-1+- 3)/2}}}
x=-2  or  x=1/2.


Vertical asymptote?  Where is the function undefined?