1. ## Exponential function requirements

Why do we require that $a$ be a non-negative number in the general expression of an exponential function,

$y = C \cdot a^x \, .$

I understand that a negative value for $a$ would give a very strange function that would fluctuate between negative and positive $y$-values which in a certain context would make no sense. But I would like to know, purely mathematically speaking, why $a$ has to non-negative.

2. ## Re: Exponential function requirements

What is $(-1)^{1/2}$?

3. ## Re: Exponential function requirements

Originally Posted by emakarov
What is $(-1)^{1/2}$?
I see what you did there. A complex number of course! So [tex]a/tex] must be non-negative because otherwise, for some numbers in the domain, would be mapped to the set of complex numbers?