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michelle1503 Group Title

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?

  • 2 years ago
  • 2 years ago

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

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

    • 2 years ago
  3. slaaibak Group Title
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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

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

    • 2 years ago
  5. michelle1503 Group Title
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    hahaha your South African? haha.. awesome :) sweet thanks ill wait :)

    • 2 years ago
  6. michelle1503 Group Title
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    LOL i can see by your name that you are LOOL BRILLIANT :)

    • 2 years ago
  7. Hero Group Title
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    Typing too fast is what did it

    • 2 years ago
  8. slaaibak Group Title
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    hero, it factors into (x-2) (x+2)

    • 2 years ago
  9. Hero Group Title
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    Which means no relevant asymptote has been crossed

    • 2 years ago
  10. slaaibak Group Title
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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.

    • 2 years ago
  11. slaaibak Group Title
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    Hero, I am not sure how you deduce that. but it's false.

    • 2 years ago
  12. Hero Group Title
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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.

    • 2 years ago
  13. Hero Group Title
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    Stop trying to disagree with what I say and concentrate on actually helping the student.

    • 2 years ago
  14. michelle1503 Group Title
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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

    • 2 years ago
  15. slaaibak Group Title
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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

    • 2 years ago
  16. slaaibak Group Title
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    |dw:1341172656390:dw|

    • 2 years ago
  17. slaaibak Group Title
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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

    • 2 years ago
  18. michelle1503 Group Title
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    lol thanks that made a lot of sense now haha... thanks for the help :)

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

    • 2 years ago
  20. michelle1503 Group Title
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    hahahahaha oh GOD you better not be a stormer or a sharkie.....

    • 2 years ago
  21. michelle1503 Group Title
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    haha thanks will do :)

    • 2 years ago
  22. slaaibak Group Title
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    We all know the stormers will win :)

    • 2 years ago
  23. michelle1503 Group Title
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    hahaha YOU WISHHHH... you stole habbana from us... pfft

    • 2 years ago
  24. slaaibak Group Title
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    I think of it as: He came to his senses...

    • 2 years ago
  25. michelle1503 Group Title
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    dont make me un-fan you grr lol :)

    • 2 years ago
  26. slaaibak Group Title
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    haha who's going to help you then :)

    • 2 years ago
  27. precal Group Title
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    To determine if the function crosses a horizontal asymptote: Set function equal to the horizontal asymptote and solve it.

    • 2 years ago
  28. precal Group Title
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    example:|dw:1341174113051:dw| the horizontal asym is y=3

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

    • 2 years ago
  30. precal Group Title
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    Note: As hero stated, functions never cross the vertical asymptotes.

    • 2 years ago
  31. Hero Group Title
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    Well, thank goodness someone supports me.

    • 2 years ago
  32. Hero Group Title
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    Not everyone thinks I'm a fool apparently.

    • 2 years ago
  33. precal Group Title
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    @Hero You are the best :)

    • 2 years ago
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