Question

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

Answer 1

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]}