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Math Help - Rational Function Formula

  1. #1
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    Rational Function Formula

    The graph of y = f(x) has one vertical asymptote, at x= -7 , and a horizontal asymptote at y = 21 . The graph of f crosses the x-axis once, at x = 6 , and the y-axis at y = -18 . Find the simplest possible formula for the rational function.
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  2. #2
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    Ok, we have 1 horizontal asymptote and 1 vertical asymptote, so this is a rectangular hyperbola, in the form:

    (y - b) = \frac{c}{x - a}

    The asymptotes, and thus the function, have shifted up 21 (=b) and shifted left -7 (=a).

    Thus,
    <br />
(y - 21) = \frac{c}{x + 7}

    To find c, simply substitute in a known coordinate: (6,0) or (0,-18).
    Substituting in (6,0), we get

    <br />
(0 - 21) = \frac{c}{6 + 7}
    <br /> <br />
-21 = \frac{c}{13}

    c = -21 \times 13 = -273

    Thus the equation is:
    <br /> <br />
(y - 21) = \frac{-273}{x + 7}
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  3. #3
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    Very good.....

    Quote Originally Posted by nzmathman View Post
    Ok, we have 1 horizontal asymptote and 1 vertical asymptote, so this is a rectangular hyperbola, in the form:

    (y - b) = \frac{c}{x - a}

    The asymptotes, and thus the function, have shifted up 21 (=b) and shifted left -7 (=a).

    Thus,
    <br />
(y - 21) = \frac{c}{x + 7}

    To find c, simply substitute in a known coordinate: (6,0) or (0,-18).
    Substituting in (6,0), we get

    <br />
(0 - 21) = \frac{c}{6 + 7}
    <br /> <br />
-21 = \frac{c}{13}

    c = -21 \times 13 = -273

    Thus the equation is:
    <br /> <br />
(y - 21) = \frac{-273}{x + 7}
    I thank you for your time and effort.
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