Question

How do you find the asymptotes for `y = 3/(x + 4)`?

Answer 1

vertical asymptote at x = - 4
horizontal asymptote at y = 0

Explanation:

The denominator of y cannot be zero as this would make y undefined. Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is non-zero for this value then it is a vertical asymptote.

solve: `x+4=0rArrx=-4" is the asymptote"`

Horizontal asymptotes occur as

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

divide terms on numerator/denominator by x

`(3/x)/(x/x+4/x)=(3/x)/(1+4/x)`

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

`rArry=0" is the asymptote"`
graph{(3)/(x+4) [-10, 10, -5, 5]}