35−2

2−40

-23450-2

x y

?{(3,-2), (5,4), (-2,0)}

A relation is set of ordered pairs, where one number is mapped to another number.

We need to be able to show relations in a variety of forms. In each form, there are pairs

of numbers, where one number is considered the input and the other is the

output.

I. Mappings

A Mapping looks like this:

35−2

2−40

This mapping contains three pairs: 3 is mapped onto -25 is mapped onto 4-2 is mapped onto 0

II. Tables

A Table looks like this:

This relation contains the same pairs as the mapping we just saw.

(The names at the top of the table do NOT have to be x and y!)

-23450-2

x y

III. Coordinate Graphs

A Coordinate Graph looks like this:

To plot pairs on a coordinate plane, the first number tells you how far to

the right or left of the origin to go, the second number is up or down.

(3,-2)

(5, 4)(-2,0)

IV. Sets of Ordered Pairs

A Set of Ordered Pairs looks like this:

We always put sets in braces { } and separate elements by commas. The

order is easy to determine here!

{(3,-2), (5,4), (-2,0)}

V. Input-Output Machines

An Input-Output Machine looks like this:

The arrows show which number is the first number (the input) and which is

the second (the output).

?

3

-2

Re-Writing RelationsThis relation is in mapping form.

Write a table for this relation.

-2

3

4

7

-1

0

4

4-20304

a b

7 -1

NOTE: Some relations use the same values more than once.

Re-Writing RelationsThis relation is in set form.

Draw a mapping for this relation.

{(1, 5), (0, 4), (4, 8), (-7, -3)}

-7

0

1

4

-3

4

5

8

The last relation had a pattern to it. Did you notice?

{(1, 5), (0, 4), (4, 8), (-7, -3)}

Some relations are created by some set of operations, a formula that maps one

number to another number.

Formula Relations

{(1, 5), (0, 4), (4, 8), (-7, -3)}

In each pair, the second number is 4 more than the first number, the formula

for this relation could be written:

y = x + 4.Or use different letters:

w = r + 4.

A Formula Machine

x + 4

1 0 4

5 4 8

Input:

Output:

?

2−

−4

7

14

21

1

What formula creates this relation?

2⋅x

2−

−4

7

14

21

1

What formula creates this relation?

5-1

100

1218

1173 ?

This relation follows a formula, find the formula & decide what 3 maps onto.

20

5-1

100

1218

1173 ?

The formula is “add 17 to each input”, x + 17. 3 maps onto 20.

5-1

100

1218

117? 0

What number maps onto 0?

17-

?

Find the output values if the input values are {1, 3, 5,

7}.

25+x

1

3

Input Output

1 3

?

Find the output values if the input values are {1, 3, 5,

7}.

25+x

3

4

Input Output

1 33 4

?

Find the output values if the input values are {1, 3, 5,

7}.

25+x

5

5

Input Output

1 33 45 5

?

Find the output values if the input values are {1, 3, 5,

7}.

25+x

7

6

Input Output

1 33 45 57 6