# Thread: How to find the horizontal asymptote of the following function

1. ## How to find the horizontal asymptote of the following function

f(x)=(x-2)^5 / (x+2)^3(x-4)^3

can someone not just show me the answer (i have that), but an easy way to get to it?

thanks!

2. Originally Posted by calcconfused
f(x)=(x-2)^5 / (x+2)^3(x-4)^3

can someone not just show me the answer (i have that), but an easy way to get to it?

thanks!
Here are the three cases of horizontal asymptotes:

1) If the degree of the denominator is greater than the degree of the numerator, the HA is y=0

2) If the degrees of the numerator & denominator are the same, the HA is the ratio of the leading coefficients

3) If the degree of the numerator is larger than the denominator there is not a HA

In terms of finding which it is, you can factor it all out and see what the degrees of each will be.

Hope that helps!

3. that does help but can someone break it down for me a bit?

i dont see why 1/x^6 is put in both the num and denom