Graphing y = (-2)^x

Date: 05/27/2005 at 03:32:18
From: John
Subject: graphing (-2)^x

I wanted to graph (-2)^x (or any negative number to the X power) but 
my math teacher could not provide me with a solution. 

How would I graph this?  Some points work and some don't.  I do know
that if I plug in whole numbers it will work, but if I plug in 
decimals and fractions I run into the problem of square roots of 
negative numbers.

Date: 05/27/2005 at 22:14:29
From: Doctor Vogler
Subject: Re: graphing (-2)^x

Hi John,

Thanks for writing to Dr. Math.  The trouble is that

  a^b

is not clearly defined when a is negative.  It only has meaning when b
is rational, and then only when the denominator of b is odd.  So your
function is only defined at certain rational points, and otherwise is
full of holes.  But the graph will look like two dotted lines, one of
which is

  y = 2^x

and the other is

  y = -(2^x)

because (-2)^x will always equal one of the above two values when it
is meaningful at all.  See also

  Base of an Exponential Function
    http://mathforum.org/library/drmath/view/55604.html 

If you have any questions about this or need more help, please write
back and show me what you have been able to do, and I will try to
offer further suggestions.

- Doctor Vogler, The Math Forum
  http://mathforum.org/dr.math/