What are all the asymptote of (x^2+3x-4)/ (x+2)x2+3x4x+2?

1 Answer
Jun 3, 2016

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

Explanation:

To find all the asymptotes for function y=(x^2+3x−4)/(x+2)y=x2+3x4x+2, let us first start with vertical asymptotes, which are given by putting denominator equal to zero or x+2=0x+2=0 i.e. x=-2x=2, which is the only vertical asymptote..

As the highest degree of numerator is 22 and of denominator is 11 and is higher by one degree, we have only slant / oblique asymptote is given by y=x^2/x=xy=x2x=x i.e. y=xy=x (Had the degree been equal, we would have horizontal asymptote).

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

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