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?

Question

anonymous · Answer

give us an example of such a function. Never heard of such a function.

slaaibak · Answer

A south african! Greetings!  Poseidon, they do exist, i'll give an example in a sec

slaaibak · Answer

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

anonymous · Answer

okay... $$f(x)=(x^2-5x+4)/(x^2-4)$$

anonymous · Answer

hahaha your South African? haha.. awesome :) sweet thanks ill wait :)

anonymous · Answer

LOL i can see by your name that you are LOOL BRILLIANT :)

hero · Answer

Typing too fast is what did it

slaaibak · Answer

hero, it factors into (x-2) (x+2)

hero · Answer

Which means no relevant asymptote has been crossed

slaaibak · Answer

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.

slaaibak · Answer

Hero, I am not sure how you deduce that.  but it's false.

hero · Answer

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.

hero · Answer

Stop trying to disagree with what I say and concentrate on actually helping the student.

anonymous · Answer

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

slaaibak · Answer

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

slaaibak · Answer

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