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Math Help - determine all axis intercepts and asymptotes

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    determine all axis intercepts and asymptotes

    how do you find the axis intercepts and asymptotes


    f(x)=(3x^2-2x)/(x^2-4)
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    Quote Originally Posted by oneway1225 View Post
    how do you find the axis intercepts and asymptotes


    f(x)=(3x^2-2x)/(x^2-4)

    f(x) = \frac{x(3x-2)}{(x+2)(x-2)}

    f(0) = 0 ... y-intercept

    f(x) = 0 at x = 0 and at x = \frac{2}{3} ... x-intercepts

    vertical asymptote, x = -2 and x = 2 ... (x+2)(x-2) in the denominator


    horizontal asymptote at y = 3 ... degree of the numerator = degree of the denominator ... ratio of the leading coefficients in the numerator and denominator gives you the value of the horizontal asymptote.
    Last edited by skeeter; April 8th 2009 at 01:46 PM. Reason: fixed my egregious factoring error ... (I could have swore I left that 3 inside).
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    Quote Originally Posted by oneway1225 View Post
    how do you find the axis intercepts and asymptotes


    f(x)=(3x^2-2x)/(x^2-4)
    First note that x \neq \pm 2


    X intercept:

    0 = \frac{3x^2 - 2x}{x^2 - 4}

    0 = 3x^2 - 2x

    0 = x(3x - 2)

    x = \left\{0, \frac{2}{3}\right\}.


    Y intercept:

    y = \frac{3(0)^2 - 2(0)}{0^2 - 4}

    y = \frac{0}{-4}

    y = 0.


    Asymptotes:

    x = \pm 2
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    Quote Originally Posted by skeeter View Post
    f(x) = \frac{3x(x-2)}{(x+2)(x-2)}

    f(0) = 0 ... y-intercept

    f(x) = 0 at x = 0 ... x-intercept

    vertical asymptote, x = -2 ... (x+2) in the denominator

    removable discontinuity (a "hole") at x = 2 ... (x-2) in both numerator and denominator

    horizontal asymptote at y = 3 ... degree of the numerator = degree of the denominator ... ratio of the leading coefficients in the numerator and denominator gives you the value of the horizontal asymptote.
    The numerator is 3x^2-2x or x(3x-2), not 3x^2-6x, so we have 2 vertical asymptotes and no hole. The other vertical asymptote is at x=2
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    Quote Originally Posted by oneway1225 View Post
    how do you find the axis intercepts and asymptotes
    To learn the general rules, study some online lessons on asymptotes and intercepts. Then please return here and review the solutions you were provided for this particular exercise, and confirm that you understand the concepts and methods they used.

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