# How do you find the vertical, horizontal or slant asymptotes for (x+2) /( x-1)?

Mar 13, 2016

vertical asymptote x = 1
horizontal asymptote y = 1

#### Explanation:

Vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation let the denominator equal zero.

solve : x - 1 = 0 → x = 1 is the asymptote

Horizontal asymptotes occur as lim_(x→±∞) f(x) → 0

divide numerator / denominator by x

$\frac{\frac{x}{x} + \frac{2}{x}}{\frac{x}{x} - \frac{1}{x}} = \frac{1 + \frac{2}{x}}{1 - \frac{1}{x}}$

as x ->oo " both " 2/x" and " 1/x → 0

hence asymptote is y = 1

Here is the graph of the function
graph{(x+2)/(x-1) [-10, 10, -5, 5]}