RELATIONS
Lesson 2­1a: Relations
Example
Arrow Diagram
• Bill, Keith, Mandy, and Joyce ride a bus to and from school. Bill rides bus number 16, Keith rides bus number 25, and Mandy and Joyce ride bus number 49
• This information can be represented in several ways:
Student
Bill
Keith
Mandy
Joyce
Bus Number
16
25
49
Ordered Pairs
Table of Values
• A relation involves two variables. You can determine the value of one of the variables if you know the value of the other variable.
• Relations can be expressed by:
­ a table of values
­ an arrow diagram
­ a graph
­ an equation or a formula
­ words
­ set of ordered pairs
Student
Bus Number
Bill
Keith
Mandy
Joyce
16
25
49
49
(Student, Bus Number)
(Bill, 16)
(Keith, 25)
The members of (Mandy, 49)
each pair are written in the same (Joyce, 49)
order
A set of ordered pairs is a RELATION
1
Example 1
Represent the relation as a set of ordered pairs
Points
Game
2
3
5
­1
6
­4
SOLUTION:
YOU TRY
(Game, Points)
(2,3)
(5,­1)
(6,3)
(9,­4)
Write five ordered pairs (distance, Income) that belong to the relation I = 45 + 0.27d
I 45 + 0.27d
=45+0.27﴾­2﴿
=44.46
­1
44.73
0
45
1
45.27
2
45.54
16
2
4
­2
y
­3x + 2
­2
­3(­2)+2=8
0
2
2
­4
4
­10
YOU TRY!
(Number, Square)
(4,16)
(2,4)
(­2,4)
(­4,16)
Write five ordered pairs (distance, time) that belong to the relation t = 5 + .4d
SOLUTION:
(Distance, Income)
(­2, 44.46)
(­1, 44.73)
(0, 45)
(1, 45.27)
(2, 45.54)
Make a table of values for y = ­3x + 2. For x, use the values {­2,0,2,4}. Then, write the set of ordered pairs.
Example 3
x
SOLUTION:
4
­4
Example 2
­2
Square
Number
9
d
Represent as a set of ordered Pairs
SOLUTION:
(x, y)
(­2, 8)
(0, 2)
(2, ­4)
(4, ­10)
SOLUTION:
d
YOU TRY
x
t
5+.4d
(Distance, time)
(­2, 4.2)
(­1, 4.6)
(0, 5)
(1, 5.4)
(2, 5.8)
Make a table of values for y = 2x ­ 3. For x, use the values {­2,0,2,4}. Then write the set of ordered pairs.
SOLUTION:
­2
0
2
4
2