# 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: $f(x)=\left\{\begin{array}{cc}x+3 \ \mbox{if} \ x < -2\\x-3\mbox{ if } x\geq-2\end{array}$
the answer says that -2 is included in the domain $(-\infty,-2]$ if $x<-2$, but -2 is not included in the domain $(-2,\infty)$ if $x\geq-2$, shouldn't it be the other way around?
I don't know, I hope it's just me. Basically the dot on the the line at the coordinates (-2,1) has a closed circle, and the dot on the line at (-5,-2) has an open circle. I'd make a graph of it, but I'm not sure how to do that on this forum. I just thought it would be an open circle at (-2,1) and an closed circle at (-2,-5) with a range of $(-\infty,\infty)$.