Section 1 – Intro to Relations and Functions

  A relation is a pairing of two elements. Relations can be expressed using ordered pairs, such as (x, y). In mathematics we expect ordered pairs to be the pairing of numeric values, such as (1, 2). However, they can be the pairing of any two pieces of data. When you have a collection of ordered pairs they form a relation.

  The first element of an ordered pair is called the input and comes from the domain of the relation. The second element of an ordered pair is called the output and comes from the range of the relation.

{ (input , output) }

{ (domain , range) }

Ex1: A relation of U.S. states to their senators would look like:

{ (NJ , Cory Booker) ; (NJ , Bob Menendez) ; (PA , Pat Toomey) ; (NY , Chuck Schumer) }

Domain = {NJ , PA , NY}

Range = {Cory Booker , Bob Menendez , Pat Toomey , Chuck Schumer}

Ex 2: A relation of automotive makes and models:

{ (Ford, Mustang) ; (Chevy, Camaro) ; (Chevy , Corvette) ; (Dodge, Challenger) }

Domain = {Ford, Chevy, Dodge}

Range = {Mustang, Camaro, Corvette, Challenger}

Relations permit the pairing of multiple elements from the range with the same element from the domain. However, functions do not.

 A function is a relation with the property that each element of the domain is paired to exactly one element in the range.

Examples of Functions:

Ex 3: A collection that pairs Student ID’s with Student Names.

Ex 4: A collection that pairs Planets with the number of moons.

In both Ex 3 and Ex 4, the input values are unique and never repeat. The output values on the other hand may or may not repeat and that is okay for the description is still representative of a function.