Relations and Functions

Core Concepts of Relations

Definition

: A rule that pairs elements of one set (Domain) with

elements of another (Co-domain).

Domain

: The set of all input values ( -values).

Range

: The set of output values ( -values) that are actually mapped

from the domain.

Co-domain

: The entire set of potential output values.

Representations

:

Mapping Diagrams

: Visual arrows connecting sets.

Ordered Pairs

: .

Tables & Graphs

: Plotting points on a coordinate plane.

Defining a Function

The Rule

: A function is a specific type of relation where

each

element in the domain

is paired with

exactly one element in the

range

.

Vertical Line Test

: A graphical method to identify a function. If any

vertical line intersects the graph at more than one point, the relation

is

not

a function.

Evaluating a Function

x

y

(

x

,

y

)