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Math Help - How to plot (-1)^x in Matchematica?

  1. #1
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    How to plot (-1)^x in Matchematica?

    I'm having a hard time trying to plot (-1)^x in Mathematica. The output appears to be empty.

    Plot[(-1)^x, {x, -10, 10}, PlotRange -> 2]

    Shouldn't this graph be continuous on intervals of the form [n, n+1) where n is an integer?
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  2. #2
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    Quote Originally Posted by Ontolog View Post
    I'm having a hard time trying to plot (-1)^x in Mathematica. The output appears to be empty.

    Plot[(-1)^x, {x, -10, 10}, PlotRange -> 2]

    Shouldn't this graph be continuous on intervals of the form [n, n+1) where n is an integer?
    No consider the interval [0,1]

    and consider the points x=2^{-n}=\sqrt[2n]{-1}, n \in \mathbb{N}

    This will be imaginary but

    x=3^{-n}=\sqrt[3n]{-1}, n \in \mathbb{N}

    will be real.
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  3. #3
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    Is there any way to graph (-1)^x in a meaningful way? I originally came across it because of its usefulness when applied over the natural numbers since it alternates between 1 and -1. However I'm curious how to visualize the general graph of this function, so I suppose it would require a graph on the complex plane which I have no idea how to do.
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  4. #4
    Behold, the power of SARDINES!
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    Quote Originally Posted by Ontolog View Post
    Is there any way to graph (-1)^x in a meaningful way? I originally came across it because of its usefulness when applied over the natural numbers since it alternates between 1 and -1. However I'm curious how to visualize the general graph of this function, so I suppose it would require a graph on the complex plane which I have no idea how to do.
    Here is Wolfram Alpha's plot

    plot (-1)^x - Wolfram|Alpha
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  5. #5
    MHF Contributor chisigma's Avatar
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    Quote Originally Posted by Ontolog View Post
    I'm having a hard time trying to plot (-1)^x in Mathematica. The output appears to be empty.

    Plot[(-1)^x, {x, -10, 10}, PlotRange -> 2]

    Shouldn't this graph be continuous on intervals of the form [n, n+1) where n is an integer?
    Try (-1)^{x} = e^{i\ \pi\ x} ... or , which of course is the same, (-1)^{x} = \cos \pi x + i\ \sin \pi x...

    Kind regards

    \chi \sigma
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