Stand Quietly

Lesson 6.1_Relations and Functions Standard: CCSS.8.F.1. Students will be able to distinguish between relations that are functions and those that are not functions.

Warm-Up #17 (4/3/17) Use substitution method to solve for x and y. y=4x and 2x+3y=28 Is (1, -4) a solution to 2x – y= 6 Name three forms of linear equations that you have learned.

Homework (4/3/17) Textbook Big Ideas page 246 #3-12 ALL

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

1-6 Relations and Functions An ordered pair consist of a x and y- coordinate A relation may be viewed as ordered pairs, mapping design, table, graph, equation, or written in sentences x-values are inputs, domain, independent variable y-values are outputs, range, dependent variable 2/23/2019 3:23 AM 1-6 Relations and Functions

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

(-3,8) (-2,8) (0,-6) (3,5) -3 -2 3 -6 5 8 Domain Range Three other ways to represent a relation: Domain Range -3 -2 3 -6 5 8 1. Mapping: (-3,8) (-2,8) (0,-6) (3,5)

Three other ways to represent a relation: 2. Table: domain range (-3, 8) (-2, 8) (0, -6) (3, 5) x y -3 -2 3 8 -6 5

A B A (-1,4) B (2,2) C (-4,-2) D (0,-3) C D Three other ways to represent a relation: 3. Graph: A B A (-1,4) B (2,2) C (-4,-2) D (0,-3) C D

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)

Is a relation a function? Focus on the x-coordinates, when given a relation. If the set of ordered pairs have different x-coordinates, it IS A function If the set of ordered pairs have same x-coordinates, it is NOT a function Y-coordinates have no affect of determining functions 2/23/2019 3:23 AM 1-6 Relations and Functions

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),(5,5),(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.

1-6 Relations and Functions Example 1 What is the domain? {0, 1, 2, 3, 4, 5} What is the range? {-5, -4, -3, -2, -1, 0} 2/23/2019 3:23 AM 1-6 Relations and Functions

1-6 Relations and Functions Example 2 4 –5 9 –1 Input –2 7 Output What is the domain? {4, -5, 0, 9, -1} What is the range? {-2, 7} 2/23/2019 3:23 AM 1-6 Relations and Functions

1-6 Relations and Functions Example 3 :00 Is this a function? Hint: Look only at the x-coordinates YES 2/23/2019 3:23 AM 1-6 Relations and Functions

1-6 Relations and Functions :40 Example 4 Is this a function? Hint: Look only at the x-coordinates NO 2/23/2019 3:23 AM 1-6 Relations and Functions

1-6 Relations and Functions :40 Example 5 Which mapping represents a function? Choice One Choice Two 3 1 –1 2 2 –1 3 –2 Choice 1 2/23/2019 3:23 AM 1-6 Relations and Functions

1-6 Relations and Functions Example 6 Which mapping represents a function? A. B. B 2/23/2019 3:23 AM 1-6 Relations and Functions

1-6 Relations and Functions Example 7 Which situation represents a function? a. The items in a store to their prices on a certain date b. Types of fruits to their colors A fruit, such as an apple, from the domain would be associated with more than one color, such as red and green. The relation from types of fruits to their colors is not a function. There is only one price for each different item on a certain date. The relation from items to price makes it a function. 2/23/2019 3:23 AM 1-6 Relations and Functions