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


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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