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

[Gregory.gags]

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" ?

 

[Number Nine]

What does it look like when you graph it on paper? Try doing it.

 

[Gregory.gags]

i did it and it's just a mirror image of 2^x

 

[Mark44]

i did it and it's just a mirror image of 2^x

I don't think so.

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

(-2)^x has values that are not real for most values of x.

 

[Number Nine]

i did it and it's just a mirror image of 2^x

Are you sure? What is (-2)^3/2?

 

[Peppino]

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.

 

[Gregory.gags]

I really don't understand? (-2)^3/2 in undefined, but i can still do (-2)^2 and get 4?

 

[Chopin]

Whenever [itex]x[/itex] is an integer, [itex](-2)^x[/itex] will be a real number, and thus will be something you can plot on a graph. For any other value of [itex]x[/itex], 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.

 

[Gregory.gags]

okay, i understand that now, but what is the significance of taking the root of a number in this situation?

 

[Mark44]

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 a^x as a^3/2. (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.