How do you find the horizontal asymptote for #f(x) = (3x) / (x+4)#?

1 Answer
Nov 18, 2015

Answer:

I found #y=3#

Explanation:

The horizontal asymptote is a line towards which the curve, described by your function, tends to get as near as possible.

To find it you can try to see what happens to your function when #x# becomes VERY big....and see if your functions "tends" to some kind of fixed value:
as #x# becomes very big, say #x=1,000,000# you have:
#f(1,000,000)=(3*1,000,000)/(1,000,000+4)#
let us forget the #4# that is negligible compared to #1,000,000#; you have:

#f(1,000,000)=(3*cancel(1,000,000))/(cancel(1,000,000))=3#

So when #x# becomes very big positively (and negatively, you can try this) your functions "tends" to get near the value #3#!
So the horizontal line of equation #y=3# will be your asymptote!

You can plot your function and see this tendency!
graph{(3x)/(x+4) [-41.1, 41.07, -20.56, 20.53]}