To understand a piece wise function is simple. Whenever you are given a value of x, to know f(x), see which of the given range x belongs to and then substitute for x in that equation...
Here say I want f(1), then observe that the definition says f(x) = 3 when x = 1, which means f(1) = 3.
To know f(-1), observe that definition says whenever x is between -2 and 1, f(x) is x+3. So f(-1) = -1+3 = 2
Now can you try f(3)?