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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


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 

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 
Associated Topics:
High School Exponents
High School Number Theory

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