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Math Help - need help creating a rational function (no clue where to start)

  1. #1
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    need help creating a rational function (no clue where to start)

    lim f(x) = 2 x -> infinty
    lim f(x) = -2 x-> - infinty
    lim f(x) = - infinty x-> -4
    lim f(x) = - infinty x-> 2-
    lim f(x) = infinty x-> 2+


    relative min of 0 at x=2
    relative max of -0.900466 at x=0.442818
    concave down (-infinty, -4) (-4,-2) (6.835351, infinty)
    concave up (2,6.835351)
    x-inter (4,0)
    y-inter (0,-1)
    vertical asymptotes at x=2, x=4
    Attached Thumbnails Attached Thumbnails need help creating a rational function (no clue where to start)-photo0217.jpg  
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  2. #2
    MHF Contributor

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    The fact that "lim f(x) = - infinty as x-> -4" and "lim f(x) = - infinty as x-> 2-" tells you that there must be factors of (x+ 4) and (x- 2) in the denominator. Further, since the limit, as x goes to 4 from "both sides" is -\infty there must be a factor of (x+ 4)^2 in the denominator. That means that the degree of the denominator is at least 3. In order that the limits as x goes to +\infty and -\infty be non-zero real numbers, the degree of the numerator and denominator must be the same. I suggest you write the function as
    \frac{ax^3+ bx^2+ cx+ d}{(x- 2)(x+4)^2}
    and try to determine values for a, b, c, and d that make the other requirements true.
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  3. #3
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    Thanks so much is there a method to coming up with those numbers or is it just plug and chug
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