Why is y=(-2)^x impossible to graph?

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Homework Help Overview

The discussion revolves around the graphing of the function y = (-2)^x and the challenges associated with it, particularly in relation to real and imaginary numbers. Participants explore the implications of graphing negative bases raised to various powers.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants share their attempts to graph the function and question the nature of the outputs for different values of x, particularly focusing on integer versus non-integer inputs.

Discussion Status

The conversation is ongoing, with participants clarifying misunderstandings about the graphing process and the nature of the function. Some guidance has been offered regarding the distinction between integer and non-integer values of x, particularly in relation to real and imaginary results.

Contextual Notes

There is a focus on the implications of taking roots of negative numbers, especially when the denominator of rational numbers is even, which leads to discussions about the limitations of graphing certain values.

Gregory.gags
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I have a question about why y=(-2)x is impossible to graph and I don't know what to say because I know that with some graph paper and a chart of values I can sure graph it pretty easily but my computer graphing program won't do it. Why not? Why is it "impossible" ?
 
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What does it look like when you graph it on paper? Try doing it.
 
i did it and it's just a mirror image of 2^x
 
Gregory.gags said:
i did it and it's just a mirror image of 2^x
I don't think so.

I'm guessing that you graphed -2x, which is different from (-2)x. The graph of y = -2x is the reflection across the x-axis of the graph of y = 2x. The graph of y = 2-x is the reflection across the y-axis of the graph of y = 2x.

(-2)x has values that are not real for most values of x.
 
Gregory.gags said:
i did it and it's just a mirror image of 2^x

Are you sure? What is (-2)3/2?
 
Think about when x = 3/2, which would be y = (-2)3/2. This would be equivalent to y = √(-2)3. The square root of negative numbers involves imaginary numbers.
 
I really don't understand? (-2)^3/2 in undefined, but i can still do (-2)^2 and get 4?
 
Whenever x is an integer, (-2)^x will be a real number, and thus will be something you can plot on a graph. For any other value of x, it will involve taking the root of a negative number as Peppino said, which will result in an imaginary number that you can't plot on graph paper.
 
okay, i understand that now, but what is the significance of taking the root of a number in this situation?
 
  • #10
Gregory.gags said:
okay, i understand that now, but what is the significance of taking the root of a number in this situation?

If x is a rational number such as 3/2, then you can write ax as a3/2. (Here I'm assuming that a > 0.) This is the same as (a3)1/2 or √(a3).

If the denominator of the rational number is even, then you're going to run into problems when the radicand is negative. That even denominator translates into a square root, fourth root, and so on.
 

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