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michelle1503

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?

  • one year ago
  • one year ago

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

    • one year ago
  2. slaaibak
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    A south african! Greetings! Poseidon, they do exist, i'll give an example in a sec

    • one year ago
  3. slaaibak
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    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

    • one year ago
  4. michelle1503
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    okay... \[f(x)=(x^2-5x+4)/(x^2-4)\]

    • one year ago
  5. michelle1503
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    hahaha your South African? haha.. awesome :) sweet thanks ill wait :)

    • one year ago
  6. michelle1503
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    LOL i can see by your name that you are LOOL BRILLIANT :)

    • one year ago
  7. Hero
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    Typing too fast is what did it

    • one year ago
  8. slaaibak
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    hero, it factors into (x-2) (x+2)

    • one year ago
  9. Hero
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    Which means no relevant asymptote has been crossed

    • one year ago
  10. slaaibak
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    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.

    • one year ago
  11. slaaibak
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    Hero, I am not sure how you deduce that. but it's false.

    • one year ago
  12. Hero
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    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.

    • one year ago
  13. Hero
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    Stop trying to disagree with what I say and concentrate on actually helping the student.

    • one year ago
  14. michelle1503
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    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

    • one year ago
  15. slaaibak
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    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

    • one year ago
  16. slaaibak
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    |dw:1341172656390:dw|

    • one year ago
  17. slaaibak
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    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

    • one year ago
  18. michelle1503
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    lol thanks that made a lot of sense now haha... thanks for the help :)

    • one year ago
  19. slaaibak
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    haha sure :) just ask if theres anything else ! oh and I hope you're not a blue bull. or pink :/

    • one year ago
  20. michelle1503
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    hahahahaha oh GOD you better not be a stormer or a sharkie.....

    • one year ago
  21. michelle1503
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    haha thanks will do :)

    • one year ago
  22. slaaibak
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    We all know the stormers will win :)

    • one year ago
  23. michelle1503
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    hahaha YOU WISHHHH... you stole habbana from us... pfft

    • one year ago
  24. slaaibak
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    I think of it as: He came to his senses...

    • one year ago
  25. michelle1503
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    dont make me un-fan you grr lol :)

    • one year ago
  26. slaaibak
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    haha who's going to help you then :)

    • one year ago
  27. precal
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    To determine if the function crosses a horizontal asymptote: Set function equal to the horizontal asymptote and solve it.

    • one year ago
  28. precal
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    example:|dw:1341174113051:dw| the horizontal asym is y=3

    • one year ago
  29. precal
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    |dw:1341174156180:dw| you will see that the function does cross the horizontal asymptote at (6, 3)

    • one year ago
  30. precal
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    Note: As hero stated, functions never cross the vertical asymptotes.

    • one year ago
  31. Hero
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    Well, thank goodness someone supports me.

    • one year ago
  32. Hero
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    Not everyone thinks I'm a fool apparently.

    • one year ago
  33. precal
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    @Hero You are the best :)

    • one year ago
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