| Summary: |
In this unit, we look at the concept of a function and introduce some important functions that are fundamental in the study of mathematics and computing. The basic idea of a function is illustrated with a simple example before presenting some more formal definitions and terminology. A function defines a relationship between the elements of two sets and we present different ways to express this relationship including arrow diagrams, formulae, graphs and lists of ordered pairs. We look at how to identify whether a relationship is a function before considering whether functions meet specific criteria that classify them as one-to-one and/or onto functions. The idea of an inverse function is then presented and we illustrate how to calculate an inverse function when it exists and interpret the results graphically. The process of combining two, or more, functions through composition is then discussed. The unit closes with a brief look at some functions that commonly occur in computing and mathematics. |
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