are all functions relations? are all relations functions?

Are all Functions Relations?

Are all Relations Functions?

Set D Set R

11

25

33

45

50

Set D Set R

11

25

33

45

50

22

50

66

90

100

Set D Set R

11

25

33

45

50

22

50

66

90

100

Set D Set R

Domain

11,25,33,45,50

11

25

33

45

50

22

50

66

90

100

Set D Set R

Domain Range

11,25,33,45,50 22,50,66,90,100

1

2

3

4

5

Set D Set R

Domain

1,2,3,4,5

1

2

3

4

5

3

4

5

Set D Set R

Domain Range

1,2,3,4,5 3,4,5

A correspondence between two sets where each element in set

D (the Domain)

is mapped to an element in set

R (the Range).

Set D Set R

Domain

Dave

Sandi

Maureen

Dorothy

Set D Set R

Domain

Dave

Sandi

Maureen

Dorothy

People

Set D Set R

Domain Range

Dave

Sandi

Maureen

Dorothy

$100

$150

$200

People Their Salaries

A FUNCTION is a special relation

Set D Set R

Each

Element

Of The

Domain

Only ONE

Element

In The

Range

Maps To

A FUNCTION is a special relation

Set D Set R

Domain Range

Dave

Sandi

Maureen

Dorothy

$100

$150

$200


Set D Set R

Domain Range

Dave

Sandi

Maureen

Dorothy

$100

$150

$200


Is this RELATION a FUNCTION?

Set D Set R

Domain{Guys}

Bob

Dave

John

Sean

Set D Set R

Domain{Guys}

Bob

Dave

John

Sean

Beth

Diane

Linda

Marcia

Range{Gals}

Guys calling Gals for a date to the Senior Ball

Set D Set R

Domain{Guys}

Bob

Dave

John

Sean

Beth

Diane

Linda

Marcia

Range{Gals}

Is the RELATION a FUNCTION?

Guys calling Gals for a date to the Senior Ball

3,2

2,3

3, 1

1,3

2, 2

3,3

1, 1

3,2

2,3

3, 1

1,3

2, 2

3,3

1, 1

Domain

3,2

2,3

3, 1

1,3

2, 2

3,3

1, 1

Domain

Range

3, 2,1, 2, 3

3,2

2,3

3, 1

1,3

2, 2

3,3

1, 1

Domain

Range

3, 2,1, 2, 3

2,3, 1, 2

Any Vertical

Line Drawn

Intersects

The Graph

No More

Than

Once

What’s the Domain? :x x R

What’s the Range

: 2 2y y

Any Vertical

Line Drawn

Intersects

The Graph

No More

Than

Once

Domain :x x R

2 2f x x x

Range : 1y y

2 2f x x x

Any Vertical

Line Drawn

Intersects

The Graph

No More

Than

Once

2 4f x x x

Domain :x x R

Range : 4y y

2 4f x x x

Set D Set R

Each

Element

Of The

Domain

Only One

Element

In The

Range

Maps To

Set D Set R

Each

Element

Of The

Domain

Only One

Element

In The

Range

Maps To

EachOnly One

Corresponds To

Set D Set R

Each

Element

Of The

Domain

Only One

Element

In The

Range

EachOnly One

Corresponds To

Set D Set R

Domain Range

Dave

Sandi

Maureen

Dorothy

$100

$150

$200


Is this ONE TO ONE ?

Any Horizontal

Line Drawn

Intersects

The Graph

No More

Than

Once

MUST be a

Function First

On your graphing calculator, graph the following and answer

2

3

3 2

4

4 2

5

5 2

1) 5 7

2) 2 2

3)

4) 4 1

5) 1

6) 5 1

7)

8) 0.3 3 2

y x

y x x

y x

y x x

y x

y x x

y x

y x x

Is it One-to-One?

Turn STAT PLOT

OFF

Zoom

6:ZStandard

On your graphing calculator, graph the following and answer

2

3

3 2

4

4 2

5

5 2

1) 5 7

2) 2 2

3)

4) 4 1

5) 1

6) 5 1

7)

8) 0.3 3 2

y x

y x x

y x

y x x

y x

y x x

y x

y x x

Is it One-to-One?

are all functions relations? are all relations functions?

Documents

senior ballset dset

peopletheir salariesis

peopletheir salariesa

functions relations

relations functions