GraphFree makes it easy to graph piecewise defined functions by specifying each piece of the function and its domain.

piecewise screenshot 1.png

Note that GraphFree now detects that the graph is actually continuous at x = 6 since the endpoints of the second and third pieces are the same, and therefore it does not add a closed circle there.

Another improvement is the ≠ option for intervals, making it a bit faster to specify removable discontinuities.

piecewise screenshot 2.png

This technique is also useful for rational functions. In the example below, the discontinuity at x = 3 is easily shown.

piecewise screenshot 3.png