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Thread: Trouble understanding "Write a function" answer

  1. #1
    Junior Member B9766's Avatar
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    Trouble understanding "Write a function" answer

    I have a problem that states,"Write a rational function $f$ having a vertical asymptote $x = 2$, a horizontal asymptote $y = 0$, and a zero at $x = 1$

    My solution was $f(x) = \frac{x-1}{(x-2)^2}$

    The answer in the book was "One possible answer is $f(x) = \frac{x-1}{(x-2)(x^2+1)}$"

    My first question: Is my answer correct?

    My second question: Why would I need the additional term of $(x^2+1)$ in the denominator other than to create a higher degree term? It seems I accomplished the same goal by squaring the $x-2$ without introducing a term that cannot produce a zero (because it would be a complex number).
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  2. #2
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    Re: Trouble understanding "Write a function" answer

    Yours seems to work as well.
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