Warming Up: Functions of a Real Variable

Sketching functions schematically is one of the most basic skills that is required of any student of science or technology. The visual impact of a plot or graph is considerable. It enables us to understand, at a glance, a good deal about the essential structure of any given functional form. Of course, we can always write a program to plot a given function, or use readily available packages for this purpose. But this is not always as instructive as sketching the functions involved in the formulas. Doing so provides insight into the nature of results derived by more formal considerations.