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Chapter 1. Functions and Preliminaries

1.1 Functions and Notation

A function is a rule that assigns to each element in a set exactly one element in a set .
The set is called the domain, and the set is called the codomain.
If a function is denoted by , we write
where is the input (independent variable) and is the output (dependent variable).
The range of is the set of all values actually taken by as varies over the domain.

Function Notation

A function can be represented in several ways:
  • Formula:
  • Graph: points in the coordinate plane
  • Table: a list of input-output pairs
  • Verbal description: a rule described in words

Example

Let .
Then:
This means that each input value is assigned exactly one output value.

Remark

A relation is a function if and only if each input corresponds to exactly one output.
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