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Thread: Domain, zeroes, and graphing to check the function

  1. #1
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    Domain, zeroes, and graphing to check the function

    Hey,
    I really need help solving this question. If someone could provide a step-by-step guide? The question asks for the domain of the function, zeroes, and to graph it to check the function.
    The function is as follows:
    x3 +x2-2x
    _________=f(x)
    2x3-x2-6x

    (The above is supposed to be those two equations divided by each other equals f(x), not really that computer savvy with typing math stuff)
    Thank you for your help!!
    Last edited by thebestrose828; Jan 6th 2017 at 02:29 PM.
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  2. #2
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    Re: Domain, zeroes, and graphing to check the function

    start by factoring numerator & denominator ...

    $f(x) = \dfrac{x(x+2)(x-1)}{x(2x+3)(x-2)}$

    note that the numerator & denominator have a common factor of $x$ ... this indicates a point discontinuity (a "hole") at $(0,1/3)$, also indicating the absence of a y-intercept.

    vertical asymptotes where $2x+3=0 \implies x = -\dfrac{3}{2}$ and where $x-2=0 \implies x = 2$

    so, domain is all real values of $x$ except $x=0$, $x=-\dfrac{3}{2}$, and $x=2$

    horizontal asymptote is determined by the ratio of the leading coefficients, $y = \dfrac{1}{2}$

    zeros where $x+2=0 \implies x=-2$ and $x-1=0 \implies x=1$
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