Question

How do you find the vertical, horizontal and slant asymptotes of: `y = (3)/(x+2)`?

Answer 1

vertical asymptote x = -2
horizontal asymptote y = 0

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 + 2 = 0 → x = - 2 is the asymptote

Horizontal asymptotes occur as

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

divide terms on numerator/denominator by x

`(3/x)/(x/x+2/x)=(3/x)/(1+2/x)`

as `xto+-oo,yto0/(1+0)`

`rArry=0" is the asymptote"`

Slant asymptotes occur when the degree of the numerator > degree of the denominator. This is not the case here (numerator-degree 0 , denominator-degree 1 ) Hence there are no slant asymptotes.
graph{3/(x+2) [-10, 10, -5, 5]}