###### 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.

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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

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.