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Algebra

analyze the graph f(x)=(x-2)^3(x-3)^2(x-4)

a)end behavior: find the power function that the graph of f resembles for large values of absolute value of x

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Stone

  1. triple root at x=2
    double root at x=3
    root at x=4

    the graph crosses the x-axis at x=2 and x=4, but is tangent at x=3

    for huge values of x, the graph resembles that of the highest power: x^6
    f(x) -> +infinity for large x, plus or minus.

    enter the function at wolframalpha.com to see the graph

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    Steve

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