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    Domain, Continuity and the Intermediate Value Theorem

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    56. Graph the function f defined by

    -1 if x <= -1
    f(x) = x if -1 < x <= 3/2
    x^2 if 3/2 < x

    Specify the domain on which this function is continuous, and the points of discontinuity.

    62. Use the Intermediate Value Theorem to prove that the function defined by f(x) = x^3 + 4x^2 + x -1 has three real roots.

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    Solution Summary

    This shows how to graph a function and determine the interval on which it is continuous, and use the intermediate value theorem to prove a function has three roots in an attached Word document.