Example OW.DFDPC.0: You supply the functions and the "cuts."
Use the Sage or the GeoGebra figures and table below to experiment
further with functions defined by piecewise cases.
Martin Flashman, Dec 20, 2013,
Created with GeoGebra
Notice how the points on the graph are paired with the points
on the mapping diagram.
Given a point / number, $x$, on the source line, there is a unique
arrow meeting the target line at the point / number, $f(x)$.
which corresponds to the function's value for $x$
Check the box in GeoGebra to see more points and arrows
corresponding to data on the table.
You can change the function and the values of $a$ and $b$ where the
"steps" occur to explore this further.