Piecewise functions are a group of sub-functions that apply to a certain interval of the independent variable. They may be continuous or discontinuous. A graph is discontinuous if the graph has some breaks in it.
If you graph the piecewise functions, the graph would look like that in the picture. The values of x on the left of the graph are taken arbitrarily just to see the behavior of the function. The domain of the piecewise functions, in other words, is the coverage of its x-values. As long as the graph passes that certain x-coordinate, it is part of its domain. Note that you use the '(' or ')' when it is not inclusive, while you use '[' or ']' if it is. The domain is inclusive when you only use ≤ or ≥, but not inclusive if it uses only < or >.
Therefore, the range is (2,8].
