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

Jun 15, 2016

Vertical asymptote is $x = - 3$ and horizontal asymptote is given by $y = 1$
To find all the asymptotes for function $\frac{x + 2}{x + 3}$, 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 $\frac{x}{x}$ 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 $y = 1$