Question

How do you find the vertical, horizontal or slant asymptotes for `y= 4 /( x+1)`?

Answer 1

vertical asymptote x = - 1
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 + 1 = 0 → x = - 1 is the asymptote

Horizontal asymptotes occur as

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

divide terms on numerator/denominator by x

`(4/x)/(x/x+1/x)=(4/x)/(1+1/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{4/(x+1) [-10, 10, -5, 5]}