The Concept of a Function

Students realize that an assumption of a constant rate of motion is not appropriate for all situations. Even if this is not possible, we may be able to use data from the situation to see a relationship of some kind between the values of one quantity and their matching values of the second quantity. Mathematicians call any clearly-described rule that assigns to each value of one quantity a single value of a second quantity a function. Functions could be described by words ("Assign to whole number its first digit," for example), by a table of values or by a graph (a graph or table of your height at different times of your life, for example) or, if we are lucky, by a formula.