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I am a little bit confused with the graphic of $f(x) =(-2)^x$

I know that is not defined on $\mathbb{R}$ when $x = \frac{n}{2k}$, where $n, k \in \mathbb{Z}$ but I have found a lot of different values of $x$ where I can no define it.

Please could you help me to have a general rule and an idea of how will look its graphic

how is its domain and range?

thank you

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Irrational powers are defined only for positive numbers. That's not laziness, there is a very precise reason:

$a^x = e^{\log a^x} = e^{x \log a}$

and as you may recall, the logarithm is defined only for positive values.

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