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March 29, 2017

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Given the function f(x)= x^3+8/x^2+-6, determine the eqaution of the asymptotes and state the end behaviours of the graph near the asymptotes.

  • grade 12 math - ,

    check you typing.

    did you mean
    f(x) = (x^3 + 8)/(x^2 - 6)
    or is it the way you typed it?
    What is with the +-6 ?

  • grade 12 math - ,

    it is f(x)=x^3+8/x^2+x-6

  • grade 12 math - ,

    assuming you really do mean

    (x^3 + 8)/(x^2 + x - 6)
    = (x+2)(x^2 - 2x + 4) / (x+3)(x-2)

    It crosses the x-axis at x = -2

    there are vertical asymptotes where the denominator is zero:
    x = -3 or x=2

    as x gets large, y -> x^3/x^2 = x

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