What is the graph of (-2)^x?

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In summary, the graph of (-2)^x is undefined for non-integer values of x, but it can be represented as a spiral in the complex plane, touching the real axis at integer values of x. Different methods can be used to obtain values for (-2)^x, such as calculating with a calculator or using complex numbers.
  • #1
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
 
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  • #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..
 
  • #3
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!
 
  • #4
Can the function be graphed in the complex plane, or is it truly undefined for nonintegral x values?
 
  • #5
You can obtain values of (-2)^x for any x, but your calculator needs a little help because you obtain complex values:

(-2)^x
= (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.
 

1. What is the shape of the graph of (-2)^x?

The graph of (-2)^x is a non-linear curve. It is an exponential function that decreases as x increases.

2. Does the graph of (-2)^x have a y-intercept?

Yes, the graph of (-2)^x intersects the y-axis at the point (0,1).

3. What is the domain of the graph of (-2)^x?

The domain of the graph of (-2)^x is all real numbers.

4. Does the graph of (-2)^x have any asymptotes?

Yes, the graph of (-2)^x has a horizontal asymptote at y=0.

5. How does changing the value of x affect the graph of (-2)^x?

As x increases, the graph of (-2)^x decreases and approaches the x-axis. As x decreases, the graph increases and approaches the y-axis.

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