Relations and functions

Relations

And

Functions

Observe the following sets.

{(2,4),(5,0),(9,8),(-1,5),(-13,-4),…}

{(-2,-4),(-1,-2),(0,0),(1,2),(2,4),…}

{(3,2),(2,1),(1,0),(0,-1),(1,2),…}

x -2 2 -2 2

y 3 4 5 6

A relation is a set of ordered pairs.

{(2,3), (-1,5), (4,-2), (9,9), (0,-6)}This is a relation

The domain is the set of all x values in the relation

{(2,3), (-1,5), (4,-2), (9,9), (0,-6)}

The range is the set of all y values in the relation

{(2,3), (-1,5), (4,-2), (9,9), (0,-6)}

domain = {-1,0,2,4,9}

These are the x values written in a set from smallest to largest

range = {-6,-2,3,5,9}

These are the y values written in a set from smallest to largest

Domain (set of all x’s) Range (set of all y’s)

1

2

3

4

5

2

10

8

6

4

A relation assigns the x’s with y’s

This relation can be written {(1,6), (2,2), (3,4), (4,8), (5,10)}

First Set: Domain( Fourth Year students)

Second Set: Range(set of positive integers)

Correspondence:Each student’s age

Maricel

Aiza

Marc Joseph

16

17

12

One- to - many

One- to - one many –to - one

Types of Relations

SPOT THE DIFFERENCE

One- to - many

FUNCTIONS

One- to - one

many –to - one

NOT a FUNCTION/S

Anne CurtisSam PintoChristine HermosaIya Villania Gorgeous

Anne CurtisSam PintoChristine HermosaIya Villania

Sam MilbyOyo Boy SottoDrew ArellanoRichard Guttierez

FUNCTIONS

Correspondence:Celebrities’ characteristic

Correspondence:Celebrity Couple

Anne CurtisSam PintoChristine HermosaIya Villania

Gorgeous

NOT FUNCTIONS

A function f from set A to set B is a rule of correspondence that assigns to each element x in the set A exactly one element y in the set B.

Set A is the domain

123

4

5

Set B is the range

2

10864

A function f from set A to set B is a rule of correspondence that assigns to each element x in the set A exactly one element y in the set B.

Must use all the x’s

A function f from set A to set B is a rule of correspondence that assigns to each element x in the set A exactly one element y in the set B.

The x value can only be assigned to one y

This is a function ---it meets our

conditions

All x’s a

re

assigned

No x has more

than one y assigned

A good example that you can “relate” to is students in our maths class this semester are set A. The grade they earn out of the class is set B. Each student must be assigned a grade and can only be assigned ONE grade, but more than one student can get the same grade (we hope so---we want lots of A’s). The example show on the previous screen had each student getting the same grade. That’s okay.

123

4

5

2

10864

Is the relation shown above a function? NO

2 was assigned both 4 and 10

A good example that you can “relate” to is students in our math class this semester are set A. The grade they earn out of the class is set B. Each student must be assigned a grade and can only be assigned ONE grade, but more than one student can get the same grade (we hope so---we want lots of A’s). The example shown on the previous screen had each student getting the same grade. That’s okay.

Determine whether the given relation is a function or not.

{(2,4),(5,0),(9,8),(-1,5),(-13,-4),…}

{(-2,-4),(-1,-2),(0,0),(1,2),(2,4),…}

{(3,2),(2,1),(1,0),(0,-1),(1,2),…}

x -2 2 -2 2

y 3 4 5 6

GRAPHS

Function Not FunctionVertical Line Test

ONE POINT

TWO/ MORE POINTS

Skill BoosterA. Identify if the given set is a function or not.

1. Place Tourist Spots

Albay Chocolate Hills

Bohol Fort Santiago

Banaue Tiwi Hot Spring

Ilocos Norte Banaue Rice Terraces

Baguio Malacaήang of the North

Manila Luneta Park

Mayon Volcano

Camp John Hay

1. Student Grade in Math

Ana 85

Joey

Joy 89

Ezra

Avin 90

Skill BoosterA. Identify if the given set is a function or not.

1. Player Sports

Nepomuceno Basketball

Pacquiao Fencing

Jaworski Boxing

Gomez Bowling

Skill BoosterA. Identify if the given set is a function or not.

4. {( 1,2), (1,4),(3,2),(3,5)}

5. {(5,2),(4,1),(3,0), (4,2)

6. {(-1,-1),(0,0),(1,-1),(2,2)}

7.

8.

Skill BoosterA. Identify if the given set is a function or not.

X 0 -1 1 -2

Y 1 2 2 4

X -2 0 4 5

Y -1 1 5 6

Skill BoosterB. Which graph shows a function? Why?

1. The range is 2 less than the domain.

1. Twice the domain is the range.

3. The range is 3 more than twice the domain.

Skill BoosterC. Construct a table of values for the following

conditions.

x

y

x

y

x

y

Seatwork:A. Determine whether the relation is a

function or not.1. Domain: Students

Correspondence: Birthdate

Range: Days of the year

2. Domain: people in the city

Correspondence: color of the eyes

Range: set of colors

1. Domain: Students

Correspondence: grade in Science

Range: positive integers

4. Domain: set of integers

Correspondence: Square root of the number

Range: Set of real numbers

5. Domain: Set of integers

Correspondence: double each number Range: set of integers

Challenging Tasks:A. Determine whether the relation is a

function or not.

B. 1. What is the greatest number of x-intercepts that a function may have ? y –intercepts? Explain your answer.

2. Is ( x + 2 ) 2 + ( y – 3) 2 = 9 a function? Explain your answer.