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

Jun 3, 2016

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]}