Math Forum: Lee: Lesson 1 - Do it by Functions, part 1

Function
What is a function? You may be thinking of something like
	(1)
that you learned in your algebra class. In fact, this is a good example of math function that we will study later. In general, function is a black box which is promised to do specific task(s), each and every time we ask it to do. We call it black because we really don’t care how it does, as long as it does as promised. You give something to the black box as input, and it returns the result as output, as shown by the schematic function diagram in figure 1.

Figure 1. Function
For instance, a washing machine is a function “to clean.” We put dirty clothes in it and out come the clean clothes. Of course, there are different brands, wash cycles, sizes, colors, etc. But they are not really relevant to the basic functionality, so we represent a typical washing machine by the function diagram in figure 2.

Figure 2. Washing machine