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What the graph of (-2)^x is

  1. Sep 25, 2003 #1
    Can some one tell me what the graph of (-2)^x is i tryed but i only got errors.

    Thank in advance for your help

    Last edited by a moderator: Feb 6, 2013
  2. jcsd
  3. Sep 25, 2003 #2
    what do you mean by "what is the graph"?

    just take some values of x, work out y with a calculator and draw it on some graph paper!

    or write a few program lines..
  4. Sep 25, 2003 #3


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    Science Advisor

    I wonder if Jonnylane tried doing that himself! If you try to graph y= (-2)x by plotting values, you can calculate values for integer values of x but that won't necessarily tell you the true graph. In this case it certainly doesn't!

    If you try to use a calculator to calculate values for fractional x, you are going to get more error messages.

    In general, the function ax is only defined for positive a. (-2)x is going to be undefined for almost all x!
  5. Sep 25, 2003 #4
    Can the function be graphed in the complex plane, or is it truly undefined for nonintegral x values?
  6. Sep 25, 2003 #5


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    Staff Emeritus
    Gold Member

    You can obtain values of (-2)^x for any x, but your calculator needs a little help because you obtain complex values:

    = (2ei[pi])x
    = 2x (ei[pi])x
    = 2x (cos([pi]x) + i sin([pi]x))

    Which is a spiral in the complex plane, which touches the real axis for all integer values of x.
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