How do you find the Vertical, Horizontal, and Oblique Asymptote given #y= (x + 2) / (x + 3)#?

1 Answer
Jun 15, 2016

Answer:

Vertical asymptote is #x=-3# and horizontal asymptote is given by #y=1#

Explanation:

To find all the asymptotes for function #(x+2)/(x+3)#, let us first start with vertical asymptotes, which are given by putting denominator equal to zero or #x+3=0# i.e. #x=-3#..

As the highest degree of both numerator and denominator is #1# and ratio of these is #x/x# i.e. #1#, horizontal asymptote is given by #y=1#. (Had the degree of numerator been higher by one, we would have obique asymptote and not horizontal one.

Hence, Vertical asymptote is #x=-3# and horizontal asymptote is given by #y=1#
graph{(x+2)/(x+3) [-10, 10, -5, 5]}