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Subsection1.1The Definition of Function

We often want to predict values of one variable from the values of a related variable. For a more extensive treatment of functions we refer the reader to PreCalculus at Nebraska: Introduction to Functions

Definition of Function

A function is a relationship between two variables for which a unique value of the output variable can be determined from a value of the input variable.

What distinguishes functions from other variable relationships? The definition of a function calls for a unique value that is, exactly one value of the output variable corresponding to each value of the input variable. This property makes functions useful in applications because they can often be used to make predictions.

A function can be described in several different ways. In the following sections, we consider examples of functions defined by tables, by graphs, and by equations.