A relation is an operation, or series of operations, that maps one number onto another.

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

?


7}.

25x

3

4

Input Output

1 33 4

?


7}.

25x

5

5

Input Output

1 33 45 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


x

y

x

y

x

y

x

y

x

y

x

y

x

y

x

y

Function Function


x

y

x

y

x

y

x

y

x

y

x

y

x

y

x

y

Function Function Not a Function


x

y

x

y

x

y

x

y

x

y

x

y

x

y

x

y


Function


x

y

x

y

x

y

x

y

x

y

x

y

x

y

x

y


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

A relation is an operation, or series of operations, that maps one number onto another.

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