Question

How do you find the asymptotes for `y = (x + 1)/(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 set the denominator equal to zero.

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

Horizontal asymptotes occur as

`lim_(xto+-oo),ytoc" (a constant)"`

divide terms on numerator/denominator by x

`(x/x+1/x)/(x/x-1/x)=(1+1/x)/(1-1/x)`

as `xto+-oo,yto(1+0)/(1-0)`

`rArry=1" is the asymptote"`
graph{(x+1)/(x-1) [-10, 10, -5, 5]}