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

1 Answer
Aug 16, 2016

Answer:

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]}