Question

How do you find the asymptotes for `y = (4 x + 6)/(x - 1)`?

Answer 1

vertical asymptote x = 1
horizontal asymptote y =4

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),yto c" (a constant)"`

divide terms on numerator/denominator by x

`((4x)/x+6/x)/(x/x-1/x)=(4+6/x)/(1-1/x`

as `xto+-oo,yto(4+0)/(1-0)`

`rArry=4" is the asymptote"`
graph{(4x+6)/(x-1) [-20, 20, -10, 10]}