find the horizontal for f(x)?

Question

find horizontal asymptote (if any) for f(x) = ax^3 / bx^3 + cx + d

anyone? new stuff for me.

Answer 1

From your question I'm assuming your equation is
f(x)=ax^3/(bx^3+cx+d)

A horizontal asymptote is a horizontal line that the function approaches as x approaches infinity (or negative infinity), but never quite gets there. In other words,

lim f(x)=G
x->inf

or

lim f(x)=H
x->-inf


If f(x) actually follows this then y=G and y=H are your horizontal asymptotes.

For f(x)=ax^3/(bx^3+cx+d),

you should be able to see that y=a/b is your only horizontal asymptote.

Answer 2

In general, when you have a rational function (one polynomial over the other), there are three cases for finding horizontal asymptotes (HA's):

1) If there is a higher power in the bottom than on the top, the HA is always y = 0 (the x-axis)

2) If there is a higher power on the top than on the bottom, there is no HA.

3) If the highest power on the top is the same as the highest power on the bottom, the HA is the line y = M/N, where M is the coefficient of the highest power on the top, and N is the coefficient of the highest power on the bottom. For example, if you had f(x) = (3x^2 - 5)/(7x^2 + 11x - 15), the HA would be y = 3/7.

Now that you know how, you find your answer.

Answer 3

Dividing numerator by denominator gives:-
f(x) = a/b - (acx/b + ad/b) / (bx² + cx + d)
as x-->∞ f(x)--> a/b
Horizontal asymptote is y = a/b

Answer 4

It's YOUR assignment....YOU find it.