A minor but cute point:

if you plot a piecewise linear function by sampling points,
and you don't sample the corners/knots,
then you will get aliasing:
the corners will be cut off, yielding -two- corners.
[and this really is aliasing!]
This is a simple illustration of the dangers of discretization
and resampling.

(Why is this is "calc"?
 B/c it's basic function info,
 esp. for people who plot functions in a spreadsheet)