Piecewise Function confusion

I'm confused about this problem in my precalc class. I already know what the answer is, but I don't understand why with the equation: $\displaystyle f(x)=\left\{\begin{array}{cc}x+3 \ \mbox{if} \ x < -2\\x-3\mbox{ if } x\geq-2\end{array}$

the answer says that -2 is included in the domain $\displaystyle (-\infty,-2]$ if $\displaystyle x<-2$, but -2 is not included in the domain $\displaystyle (-2,\infty)$ if $\displaystyle x\geq-2$, shouldn't it be the other way around?