What is a Function? The Difference between Functions and Relations – Practice Problems

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A relation is a way of expressing a connection or relationship between any two pieces of information.

A function is a particular kind of relation between sets. A function takes every element x in a starting set, called the domain, and tells us how to assign it to exactly one element y in an ending set, called the range.

For example, each person is in the following table is paired with a number representing his or her height:

Alex → 180
Claudia → 165
Gilbert → 204
Judith → 165

The given relation {(Alex, 180), (Claudia, 165), (Gilbert, 204), (Judith, 165)} is a function as every person is pairs with exactly one number, their height. The domain is (Alex, Claudia, Gilbert, Judith). The range is (165, 180, 204).

Remember that all functions are relations, but not all relations are functions. For instance, matching a person’s age with their height does not give a function: Say Claudia and Gilbert are both 15. In this case, 15 would get paired with both 165 and 204, meaning that every age is not paired with exactly one height.

Understand the concept of a function and use function notation.

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Exercises in this Practice Problem
Describe Herman's problems with the vending machine.
Explain the difference between functions and relations.
Decide which mapping diagrams represent a function.
Identify which statements are describing a function.
Find three main facts about functions.
Determine if the assignment is a function or relation.