Question

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

Answer 1

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]}