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Math Help - Continuosity

  1. #1
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    Talking Continuosity

    My Cal. 1 professor gave us this as an extra credit on one of our quizzes, however since no one got the correct answer, he didn't tell us how to find it.

    Let "f" be a function defined by
    x, if x is rational
    f(x)=
    -x, if x is irrational

    Sketch the graph of this function as best you can and decide where is is continuos.

    I'm not sure exactly how this graph would look, can anyone please help.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ERiveraSr View Post
    My Cal. 1 professor gave us this as an extra credit on one of our quizzes, however since no one got the correct answer, he didn't tell us how to find it.

    Let "f" be a function defined by
    x, if x is rational
    f(x)=
    -x, if x is irrational

    Sketch the graph of this function as best you can and decide where is is continuos.

    I'm not sure exactly how this graph would look, can anyone please help.
    this is similar to the Dirichlet function

    maybe these will give you some ideas

    see here

    and here

    and here
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