Given a function, how do you test for Horizontal Asymptotes...?

The third answer above is close, but not quite right. A function can have two different horizontal asymptotes -- one in the limit of +infinity, and the other in the limit of -infinity. You need to check the values of both limits separately.

For instance, the horizontal asymptotes of arctan(x) are +pi/2 (as x -> +infinity) and -pi/2 (as x -> -infinity).

For rational functions (functions that can be expressed as the ratio of two polynomials) there is an easy way to test for and find the horizontal asymptotes:

Let f(x) = p(x)/q(x) be a rational function. Then:

1. If (the degree of q(x)) > (the degree of p(x)) then there is one horizontal asymptote at 0.

2. If (the degree of q(x)) = (the degree of p(x)) then there is one horizontal asymptote at the (leading coefficient of p(x))/(leading coefficient of q(x))

3. If (the degree of p(x)) < (the degree of q(x)) then there is no horizontal aymptote.

Horizontal Asymptote Test

set the function equal to zero and solve for x.then go back and check each answer.the ones that dont work are you asymptotes or if your looking at the graph you can see where the function is and it wont pass that point.have a nice day.I know it's right,i did it before and i made sure 2 before i put it from my 22 year old brother.who took this class and passed it with a a.so..

Solve equation for x. anything (y-a) in the denominator gives a horizontal asymptote at y = a.

Check the value of f(x) as x tends to +/- infinity. Suppose it gives u a finite value "C". Then y=C is ur horizontal asymptote.

By lying down?

my head hurts!