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Thread: How do I write an equation with a slant asymptote?

  1. #1
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    How do I write an equation with a slant asymptote?

    Hi everyone,

    We recently learned in math class that to get the equation of a slant asymptote of an equation, divide the numerator by the denominator. I'm understanding how to divide polynomials, but now I get a freeform homework question that says write an equation of a function with a slant asymptote of y = x ! How do I do this? I'm used to going the other way!

    Thanks
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  2. #2
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    Quote Originally Posted by gobbajeezalus View Post
    Hi everyone,

    We recently learned in math class that to get the equation of a slant asymptote of an equation, divide the numerator by the denominator. I'm understanding how to divide polynomials, but now I get a freeform homework question that says write an equation of a function with a slant asymptote of y = x ! How do I do this? I'm used to going the other way!

    Thanks
    If you divide the numerator by the dnominator then you get the term of the asymptote and a remainder which is approaching zero if x approaches infinity. You now have to choose such a remainder. The most simple case is that
    r = \dfrac1x

    Therefore the equation of the function is:

    y = x + \dfrac1x = \dfrac{x^2+1}x

    But of course you can choose

    r = \dfrac{2x+3}{x^3+x^2}

    Then the function is

    y = x+ \dfrac{2x+3}{x^3+x^2} = \dfrac{x^4+x^3+2x+3}{x^3+x^2}
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