are all functions relations? are all relations functions?
Post on 21-Jan-2016
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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
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
1
2
3
4
5
3
4
5
Set D Set R
Domain Range
1,2,3,4,5 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
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
People Their Salaries
Set D Set R
Domain Range
Dave
Sandi
Maureen
Dorothy
$100
$150
$200
People Their Salaries
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}
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
Any Vertical
Line Drawn
Intersects
The Graph
No More
Than
Once
Any Vertical
Line Drawn
Intersects
The Graph
No More
Than
Once
Any Vertical
Line Drawn
Intersects
The Graph
No More
Than
Once
Any Vertical
Line Drawn
Intersects
The Graph
No More
Than
Once
Any Vertical
Line Drawn
Intersects
The Graph
No More
Than
Once
Any Vertical
Line Drawn
Intersects
The Graph
No More
Than
Once
Any Vertical
Line Drawn
Intersects
The Graph
No More
Than
Once
Any Vertical
Line Drawn
Intersects
The Graph
No More
Than
Once
Any Vertical
Line Drawn
Intersects
The Graph
No More
Than
Once
Any Vertical
Line Drawn
Intersects
The Graph
No More
Than
Once
Any Vertical
Line Drawn
Intersects
The Graph
No More
Than
Once
Any Vertical
Line Drawn
Intersects
The Graph
No More
Than
Once
Any Vertical
Line Drawn
Intersects
The Graph
No More
Than
Once
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
Any Vertical
Line Drawn
Intersects
The Graph
No More
Than
Once
Any Vertical
Line Drawn
Intersects
The Graph
No More
Than
Once
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
Range : 1y y
2 2f x x x
Any Vertical
Line Drawn
Intersects
The Graph
No More
Than
Once
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
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
People Their Salaries
Is this ONE TO ONE ?
Any Horizontal
Line Drawn
Intersects
The Graph
No More
Than
Once
Any Horizontal
Line Drawn
Intersects
The Graph
No More
Than
Once
Any Horizontal
Line Drawn
Intersects
The Graph
No More
Than
Once
Any Horizontal
Line Drawn
Intersects
The Graph
No More
Than
Once
Any Horizontal
Line Drawn
Intersects
The Graph
No More
Than
Once
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?
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