Question

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

Answer 1

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

`(x/x +2/x )/(x/x - 1/x) = (1 + 2/x)/(1 - 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]}