2. Relation
A relation is a set of ordered pair (x,y).
A relation is a rule that relates values from a set
of values (called the domain) to a second set of
values (called the range).
The elements of the domain can be imagined as
input to a machine that applies a rule to these
inputs to generate one or more outputs.
R = {(1,2), (2,4), (3,6), (4,8), (5,10)}
3. A relation as a subset
Let A = {1, 2} and B = {1, 2, 3} and define a relation R
from A to B as follows: Given any (x, y) A x B.
(x, y) R means that is an integer.
1. State explicitly which ordered pairs are in R.
2. Is 1 R 3? Is 2 R 3? Is 2 R 2?
3. What are the domain and range of R?
4. A relation as a subset
Let A = {1, 2} and B = {1, 2, 3} and define a relation R
from A to B as follows: Given any (x, y) A x B. (x, y)
R means that is an integer.
1. State explicitly which ordered pairs are in R.
A x B = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2,
3)}
(𝟏, 𝟏)
𝟏−𝟏
𝟐
=
𝟎
𝟐
=𝟎∴(𝟏, 𝟏) ∈ 𝑹
11. A relation as a subset
Let A = {1, 2} and B = {1, 2, 3} and define a relation R
from A to B as follows: Given any (x, y) A x B. (x, y)
R means that is an integer.
3. What are the domain and range?
A x B = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2,
3)}
𝑫𝒐𝒎𝒂𝒊𝒏 𝒐𝒇 𝑹={𝟏,𝟐}𝐚𝐧𝐝𝐭𝐡𝐞 𝐑𝐚𝐧𝐠𝐞={𝟏,𝟐,𝟑}
12. Suppose you are working in a fast food
company. You earn Php 40 per hour. Your
earnings are related to the number of hours
of work.
Example
1. How much will you earn if you work 4 hours? 5
hours? 6 hours? 7 hours? 8 hours?
2. Express each as an ordered pair.
3. Based on your answer in item 2, what is the domain
and the range?
13. Suppose you are working in a fast food company. You
earn Php 40 per hour. Your earnings are related to the
number of hours of work.
Example
1. How much will you earn if you work 4 hours? 5 hours?
6 hours? 7 hours? 8 hours?
2. Express each as an ordered pair.
3. Based on your answer in item 2, what is the domain
and the range?
4 – 160, 5 – 200, 6 – 240, 7 – 280, 8 - 320
R = {(4, 160), (5, 200), (6, 240), (7, 280), (8, 320)}
D = {4, 5, 6, 7, 8} R = {160, 200, 240, 280, 320}
14. Suppose the bicycle rental at Nijaga Park is worth Php
20 per hour. Your sister would like to rent a bicycle for
amusement?
Example
1. How much will your sister pay if she would like to
rent 3 hours? 4 hours? 5 hours? 6 hours?
2. Express each as an ordered pair.
3. Based on your answer in item 2, what is the domain
and the range?
3 – 60, 4 – 80, 5 – 100, 6 - 120
R = {(3, 60), (4, 80), (5, 100), (6, 120)}
D = {3, 4, 5, 6} R = {60, 80, 100, 120}
15. Suppose Martha is selling a fish ball at
NWSSU. Martha sell 50 fish balls per day.
Questions:
1. How many fish balls will Martha sell in
2 days? 3 days? 5 days? 1 week?
2. Express each as an ordered pair.
3. Based on answer number 2, give the
domain and the range.
29. What is a relation?
What is a domain and a range?
What are the three correspondence of
relation?
What is a one-to-one correspondence?
What is a many-to-one
correspondence?
What is a one-to-many
correspondence?
30. Function
A function is a special type of relation.
It is a relation in which every element in
the domain is mapped to exactly one
element in the range. Thus, a set of
ordered pairs is a function if no two
distinct ordered pairs have equal
abscissas.
35. The table describes
clearly the behavior of
the value of y as the
value of x changes.
Tables can be
generated based on the
graph.
TABLE OF VALUES
x y
-2 -4
-1 -2
0 0
1 2
2 4
x -2 -1 0 1 2
y -4 -2 0 2 4
47. Let’s Try!
1.A = {(1,1), (2,1), (3,5), (4,7), (5,9)} FUNCTION
2. A = {(a,b), (b,d), (c,e), (c,f), (d,e)} NOT A
FUNCTION
x 1 4 8 10 12
y 2 4 6 8 10 FUNCTION
