Functions as Models

A function can serve as a simple kind of mathematical model, or a simple piece of a larger model. Remember that a function is just a rule,  f, that expresses the dependency of one variable quantity,  y, on another variable quantity,  x. We can think of the rule (given in our model as a graph, a formula, or a table of values) as a representation of some natural cause and effect relationship – if  x, then  y  – between the two variable quantities. Schematically:

In the computer model of the airplane crash, for example, there would be many functions representing the many different cause and effect relationships between the parts of the aircraft, the weather, and the pilot's actions.

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