Relations and Functions Standard: M8A3 c. Distinguish between relations that are functions and those that are not functions.

Relation = { (3,5),(-2,8),(-3,8),(0,-6) } A ________ is a set of __________________. relation ordered pairs Relation = { (3,5),(-2,8),(-3,8),(0,-6) } The ________ is the ______ of ______ values. domain set x The ________ is the ______ of ______ values. range set y

Domain: { ____, ____, ___, ____} EXAMPLE Relation = { (3,5),(-2,8),(-3,8),(0,-6) } Domain: { ____, ____, ___, ____} Range: {____ , ___, ____}

Domain: { ____, ____, ___, ____} -3 -2 3 EXAMPLE Relation = { (3,5),(-2,8),(-3,8),(0,-6) } Domain: { ____, ____, ___, ____} -3 -2 3 Range: {____ , ___, ____}

Domain: { ____, ____, ___, ____} -3 -2 3 EXAMPLE Relation = { (3,5),(-2,8),(-3,8),(0,-6) } Domain: { ____, ____, ___, ____} -3 -2 3 Range: {____ , ___, ____} -6 5 8

-3 -2 3 -6 5 8 Domain Range Three other ways to represent a relation: 3 -6 5 8 1. Mapping:

x y -3 -2 3 8 -6 5 Three other ways to represent a relation: 2. Table: domain range x y -3 -2 3 8 -6 5

Three other ways to represent a relation: 3. Graph:

Example 1: Represent the following relations as a set of ordered pairs. -2 5 6 -3 2 7 { } (-2, 2) (0, -3) (5, 7) (6, 7)

{ } (2,0) (-2,2) (-2,-2) (-6, 2)

y x -3 -1 2 4 -2 3 -7 4 { } (-3,0) (-1,-2) (0,3) (2,-7) (4,4)

Functions can be represented four different ways: A ___________ is a relation in which no number in the _________ is __________. (the x-value can not repeat) function domain repeated Functions can be represented four different ways: 1. ______________ 2. ______________ 3. ______________ 4. ______________ mapping graph table set of ordered pairs

Example 2: Represent the following function as a mapping, graph, and table. {(7,4),(-3,6),(5,8),(4,3),(1,-3)} -3 3 4 6 8 -3 1 4 5 7

{(7,4),(-3,6),(5,8),(4,3),(1,-3)}

{(7,4),(-3,6),(5,8),(4,3),(1,-3)} y x -3 6 1 -3 4 3 5 8 7 4

Each element of the domain is only used once. Example 3: Are the following relations also functions? -2 3 -7 -2 3 -7 -4 5 8 -4 5 8 Each element of the domain is only used once. 3 is used twice. NOT A FUNCTION FUNCTION

Will all vertical lines cross the graph at only one point? FUNCTION Will all vertical lines cross the graph at only one point? YES. Each x is only used once.

Will all vertical lines cross the graph at only one point? D FUNCTION Will all vertical lines cross the graph at only one point? YES. Each x is only used once.

Will all vertical lines cross the graph at only one point? NOT A FUNCTION Will all vertical lines cross the graph at only one point? NO. x =-3 is used twice.

Will all vertical lines cross the graph at only one point? F NOT A FUNCTION Will all vertical lines cross the graph at only one point? NO. x =-2 is used three times.

Are all x values used only once? -4 -2 2 -3 3 1 NOT A FUNCTION Are all x values used only once? NO. x = - 4 is used twice.