Question

Does the graph of function
f(x)=4x^7+3x−4/9x^7−1003
have a horizontal asymptote? If so, find the equation of the asymptote

Answer 1

Zepdrix, I wish I could buy you a beer tongiht!

Answer 2

Soooo, for horizontal asymptotes I guess we want to see what this graph is doing at the ends.

So let's take a look.

\[\lim_{x \rightarrow \pm \infty}\frac{ 4x^7+3x-4 }{ 9x^7-1003 }\]

Answer 3

Lol, beer is gross XD chocolate milk is my drink of choice! lol

Answer 4

Even better...As a Big Cat that suits me fine too!

Answer 5

Beer is fantastic.

The solution here is very simple. Since the degree of the numerator is the same as that of the denominator, the horizontal asymptote is simply at the ratio of the coefficients of those terms.

Answer 6

Does that make sense cat? :D You can ignore the lower order terms, since they become insignificant in the limit.

What are the coefficients of the highest order terms?

Answer 7

Thanks qpHalcy0n!

Answer 8

Np, interestingly if the degree of the numerator is larger, there is no horizontal asymptote. The other way around, the asymptote is y = 0.

Answer 9

So I guess it does not have a horizontal asymptote?

Answer 10

Yes, it does.

You have a degree of 7 in the numerator, and a degree of 7 in the denominator.

Answer 11

The h/a is the ratio of their coefficients.
y = 4/9

Answer 12

If it didn't have an asymptote, then the limit would BLOW UP in one direction or another.
So if there is no asymptote, you should get an answer approaching +/- infinity.

If you understand what Hal is saying, you should be getting a nice number for your limit :)

Answer 13

I do understand that the degree's of the numerator and denominator cancel out, but I can't visualize the graph

Answer 14

does this help you visualize it maybe? :o