Post on 04-Jan-2016
A relation is an operation, or series of operations, that maps one number
onto another.
35
13
240
You can think of a relation as a machine that uses numbers
to produce other numbers.
This machine adds 5 to any number you put into it.
5x
17
22
11
6
0
5
?
2
4
7
14
21
1
What relation does this machine represent?
x2
2
4
7
14
21
1
One possibility is that each number is multiplied by –2.
?
4
2
2
1
16
8
What relation does this machine represent?
2x
4
2
2
1
16
8
One possibility is that each number is divided by 2.
5-1
100
1218
117
In this relation, -5 is mapped onto 12, 1 is mapped onto 18,
and 100 is mapped onto 117.
5-1
100
1218
1173 ?
The relation would map 3 onto which number?
20
5-1
100
1218
1173 ?
If you see the relation as adding 17 to each number, you could say that 3 maps onto 20.
5-1
100
1218
117? 0
What number maps onto 0?
5-1
100
1218
117017-
What number maps onto 0?
13 x
8
23
2
7 16? ?
?
Find the missing numbers:
13 x
8
23
2
7 16
?5
Find the missing numbers:
5
13 x
8
23
2
7 16
There is a name for the numbers that go into a relation.
Since we put them into the relation,it makes sense to call them input values.
5
13 x
8
23
2
7 16
5
13 x
8
23
2
7 16
And there is a name for the numbers that come out of a relation.
Since they come out of the relation,it makes sense to call them output values.
5
13 x
8
23
2
7 16
?
Find the output values if the input values are {1, 3, 5,
7}.
25x
1
3
Input Output
1 3
?
Find the output values if the input values are {1, 3, 5,
7}.
25x
3
4
Input Output
1 33 4
?
Find the output values if the input values are {1, 3, 5,
7}.
25x
5
5
Input Output
1 33 45 5
?
Find the output values if the input values are {1, 3, 5,
7}.
25x
7
6
Input Output
1 33 45 57 6
Relation - Any set of ordered pairs{(1,6), (2,7), (3,8), (4,9)}
Function - A special type of relation where there is exactly one output for every input. For every x, there is exactly one y.
x y
12
67
x y
12
67
Not a Function Function
yx
-2-1 0 1 2
-4-2 0 2 4
y = 2x
input output
-2-1
-4-2
01
02
2 4
x-y Chart or TableMapping Diagram
Function
Vertical Line Test - Functions
x
y
x
y
x
y
x
y
x
y
x
y
x
y
x
y
Function
Vertical Line Test - Functions
x
y
x
y
x
y
x
y
x
y
x
y
x
y
x
y
Function Function
Vertical Line Test - Functions
x
y
x
y
x
y
x
y
x
y
x
y
x
y
x
y
Function Function Not a Function
Vertical Line Test - Functions
x
y
x
y
x
y
x
y
x
y
x
y
x
y
x
y
Function Function Not a Function
Function
Vertical Line Test - Functions
x
y
x
y
x
y
x
y
x
y
x
y
x
y
x
y
Function Function Not a Function
Function
Not a Function
Function Not a Function
Not a Function
Tell whether the relation below is a function.
1)
2)
3)
4)
input output01
523
yx
-3-3-3-3
-1 0 1 2
x
y
Function
Not a Function
Not a Function
input output
-2
-1
0
3456
Not a Function