Piecewise Functions

So I'm in Calculus 1, and piecewise functions are a problem, especially graphing them and determining continuity.

f(x){1/(X^2) if x<-1
{2 if -1<X<1
{3 if X=1
{X+1 if 1<X<=2
{-1/X if X>2

Now, what I gather from this is that the first equation is continues if x is lesser then -1. But what happens if its not? In addition, what do the just 2 and 3 mean? What does 2 have to do with (-1<X<1)? And what does 3 do if what X equals 1? Can someone give me a walk through with this? I have an exam tomorrow and my teacher seems to love testing us on piecewise with little explanation as to what they do.