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

##### 1 Answer

I found

#### Explanation:

The horizontal asymptote is a horizontal line of equation:

towards which the curve described by your function TENDS to get closer and closer maybe not immediately but as

To find this line there is a trick!

Take your function and try to "see" its behavior very far from the origin...i.e. when

In your case consider a

you get:

So, you get

Your asymptote!!!

You can "see" this graphically:

graph{(4x)/(x-3) [-25.66, 25.65, -12.83, 12.83]}

The two branches of your function will get as near as possible to the horizontal line

Hope it helps!