What are the asymptote(s) of # f(x) = (3x) / (x+4)#?

1 Answer
Nov 11, 2015

Answer:

#f(x)# has horizontal asymptote #y=3# and vertical asymptote #x=-4#

Explanation:

When #x=-4# the denominator of #f(x)# is zero and the numerator is non-zero. So this rational function has a vertical asymptote #x=-4#.

#(3x)/(x+4) = 3/(1+4/x) -> 3# as #x->oo#

So #f(x)# has a horizontal asymptote #y = 3#

graph{(3x - xy - 4y)(x+4+y0.001)(y-3-x0.001) = 0 [-25.25, 14.75, -7.2, 12.8]}