Functions

Introduction

A relation is a set of inputs and outputs, often written as ordered pairs (input, output). We can also represent a relation as a mapping diagram or a graph. A function is a relation in which each possible input value leads to exactly one output value. The input values make up the Domain of a Function, and the output values make up the Range of a Function, also known as the codomain. A relation is NOT a function if one input in the domain maps to multiple outputs in the range. For example, consider the following relations: R1 = {(1,2), (1, 3), (2, 4), (3, 5)} and R2 = {(1,2), (2, 4), (3, 5), (4, 5)}. The relation R1 is not a function because the input 1 maps to both 2 and 3. However, the relation R2 is a function since each input only maps to one output. Note that multiple inputs can map to a single output; that is, R2 is still a function despite the inputs 3 and 4 both mapping to the same output, 5.

Resources

• Determining if a Relation is a Function, Lumen Learning
• Relations vs. Functions, Cliff's Notes
• Identifying Functions Using Graphs, Lumen Learning