anonymous
  • anonymous
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
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
give us an example of such a function. Never heard of such a function.
slaaibak
  • slaaibak
A south african! Greetings! Poseidon, they do exist, i'll give an example in a sec
slaaibak
  • slaaibak
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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anonymous
  • anonymous
okay... \[f(x)=(x^2-5x+4)/(x^2-4)\]
anonymous
  • anonymous
hahaha your South African? haha.. awesome :) sweet thanks ill wait :)
anonymous
  • anonymous
LOL i can see by your name that you are LOOL BRILLIANT :)
Hero
  • Hero
Typing too fast is what did it
slaaibak
  • slaaibak
hero, it factors into (x-2) (x+2)
Hero
  • Hero
Which means no relevant asymptote has been crossed
slaaibak
  • slaaibak
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
  • slaaibak
Hero, I am not sure how you deduce that. but it's false.
Hero
  • Hero
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
  • Hero
Stop trying to disagree with what I say and concentrate on actually helping the student.
anonymous
  • anonymous
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
  • slaaibak
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
  • slaaibak
|dw:1341172656390:dw|
slaaibak
  • slaaibak
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
anonymous
  • anonymous
lol thanks that made a lot of sense now haha... thanks for the help :)
slaaibak
  • slaaibak
haha sure :) just ask if theres anything else ! oh and I hope you're not a blue bull. or pink :/
anonymous
  • anonymous
hahahahaha oh GOD you better not be a stormer or a sharkie.....
anonymous
  • anonymous
haha thanks will do :)
slaaibak
  • slaaibak
We all know the stormers will win :)
anonymous
  • anonymous
hahaha YOU WISHHHH... you stole habbana from us... pfft
slaaibak
  • slaaibak
I think of it as: He came to his senses...
anonymous
  • anonymous
dont make me un-fan you grr lol :)
slaaibak
  • slaaibak
haha who's going to help you then :)
precal
  • precal
To determine if the function crosses a horizontal asymptote: Set function equal to the horizontal asymptote and solve it.
precal
  • precal
example:|dw:1341174113051:dw| the horizontal asym is y=3
precal
  • precal
|dw:1341174156180:dw| you will see that the function does cross the horizontal asymptote at (6, 3)
precal
  • precal
Note: As hero stated, functions never cross the vertical asymptotes.
Hero
  • Hero
Well, thank goodness someone supports me.
Hero
  • Hero
Not everyone thinks I'm a fool apparently.
precal
  • precal
@Hero You are the best :)

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