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Perhaps the most useful idea for modeling the real world is the concept of function. Let's look at an example. If a rock climber drops a stone from a high cliff, we know that the stone will fall. But this general description doesn't help us figure out when the stone will hit the ground. To find out, we need a rule that relates the distance d the stone falls to the time it has been falling. Galileo was the first to discover the rule: In t seconds the stone falls feet. This “rule” is called a function; we write this function as Using this function model, we can predict when the stone will hit the ground. In this chapter we study properties of functions and how function models can help us to get precise information about the thing or process being modeled.
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