What are all the asymptote of #(x^2+3x-4)/ (x+2)#?

1 Answer
Jun 3, 2016

Answer:

Vertical asymptotes is #x=-2# and obliqe asymptote is given by #y=x#

Explanation:

To find all the asymptotes for function #y=(x^2+3x−4)/(x+2)#, let us first start with vertical asymptotes, which are given by putting denominator equal to zero or #x+2=0# i.e. #x=-2#, which is the only vertical asymptote..

As the highest degree of numerator is #2# and of denominator is #1# and is higher by one degree, we have only slant / oblique asymptote is given by #y=x^2/x=x# i.e. #y=x# (Had the degree been equal, we would have horizontal asymptote).

Hence, while vertical asymptotes is #x=-2# and obliqe asymptote is given by #y=x#

graph{x+x/(x+2) [-20, 20, -10, 10]}