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can someone please explain to me when rational functions do not cross and when they do cross their horizontal asypmtote. I thought the rational function can never reach, only approach an asymptote but some rational functions completely cross their horizontal asymptote and i dont understand why this sometimes happens?

Mathematics
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give us an example of such a function. Never heard of such a function.
A south african! Greetings! Poseidon, they do exist, i'll give an example in a sec
Remember, a horisontal asymptote is there to show that the function goes to a limit when x goes to +- infinity. Will try to explain better now

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okay... \[f(x)=(x^2-5x+4)/(x^2-4)\]
hahaha your South African? haha.. awesome :) sweet thanks ill wait :)
LOL i can see by your name that you are LOOL BRILLIANT :)
Typing too fast is what did it
hero, it factors into (x-2) (x+2)
Which means no relevant asymptote has been crossed
Anyways. The explanation: The horizontal asymptote simply shows us the limit of the function when x tends to +- infinity. Now this really doesn't tell us anything about the function not evaluated in the extremities.
Hero, I am not sure how you deduce that. but it's false.
slaaibak, I was referring to the vertical asymptotes. Stop making it look like I don't know what I'm talking about. I hate when people try to belittle others. I meant that the function doesn't cross the vertical asymptotes.
Stop trying to disagree with what I say and concentrate on actually helping the student.
okay understood that it shows the limit of the function. BUT... the horizontal asymptote is y=1 and in the graph it is crossed... i dont get that ... and other graghs the Horizontal asymptote isnt crossed... what i wana know is what parts of the graph uses the horizontal asymptote as a limit as x reaches +- infinity and which parts of the graph just ignores the H.A and resembles itself as a cubic function...explain that to me.. if you understand what im trying to say lol
The horizontal asymptote is used for x when x tends to +-infinity. That means, very very very large values of x uses it as an asymptote. In words, the asymptote is something that, if you take very large values of x, the graph/function value converges to a y-value. I'll draw something quickly
|dw:1341172656390:dw|
At the two circles is what I'm trying to show. The asymptote is showing the behavior of the function when x gets either very small or very large. But, this is important, the horisontal asymptotes say nothing about the "finite" values of the function. Meaning, apart from infinity, the graph my cross the horizontal asymptote
lol thanks that made a lot of sense now haha... thanks for the help :)
haha sure :) just ask if theres anything else ! oh and I hope you're not a blue bull. or pink :/
hahahahaha oh GOD you better not be a stormer or a sharkie.....
haha thanks will do :)
We all know the stormers will win :)
hahaha YOU WISHHHH... you stole habbana from us... pfft
I think of it as: He came to his senses...
dont make me un-fan you grr lol :)
haha who's going to help you then :)
To determine if the function crosses a horizontal asymptote: Set function equal to the horizontal asymptote and solve it.
example:|dw:1341174113051:dw| the horizontal asym is y=3
|dw:1341174156180:dw| you will see that the function does cross the horizontal asymptote at (6, 3)
Note: As hero stated, functions never cross the vertical asymptotes.
Well, thank goodness someone supports me.
Not everyone thinks I'm a fool apparently.
@Hero You are the best :)

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