What does the graph of (-2)^x look like?

[reaver]

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

reaver

 

[jonnylane]

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..

 

[HallsofIvy]

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 a^x is only defined for positive a. (-2)^x is going to be undefined for almost all x!

 

[Loren Booda]

Can the function be graphed in the complex plane, or is it truly undefined for nonintegral x values?

 

[ahrkron]

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

(-2)^x
= (2e^i[pi])^x
= 2^x (e^i[pi])^x
= 2^x (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.