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michelle1503

  • 2 years ago

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?

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  1. Posideon
    • 2 years ago
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    give us an example of such a function. Never heard of such a function.

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

  3. slaaibak
    • 2 years ago
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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

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

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

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

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

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

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

  10. slaaibak
    • 2 years ago
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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.

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

  12. Hero
    • 2 years ago
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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.

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

  14. michelle1503
    • 2 years ago
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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

  15. slaaibak
    • 2 years ago
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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

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

  17. slaaibak
    • 2 years ago
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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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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