Exponential function if a<0

I am learning about exponential function from math book for high-school.

I have learned about $\displaystyle y = a^x $ if $\displaystyle a>0$ and $\displaystyle x \in R$. I have understand pretty much of it, but I didn't find any explanation if $\displaystyle a<0$ (why?).

I have tried to understand by myself properties of exponential function $\displaystyle y = a^x $ if $\displaystyle a<0$ and $\displaystyle x \in Z$.

This is what I think are properties:

1) for $\displaystyle a<0$ and $\displaystyle x =2k$ function is defined but there is no inverse function

2) for $\displaystyle a<0$ and $\displaystyle x =2k+1$ function is defined but there is inverse function

Can someone explain me a little bit about that?