Lesson 1: RELATION
Lesson Objectives:
At the end of the lesson, the students will be able to:
• define relation;
• understand the domain and the range; and
• identify the representation and correspondence of relation.
Recall:
Ordered Pair – a pair of elements x and y.
Where:
x – Abscissa or first coordinate
y – Ordinate or second coordinate
RELATION - is a collection of ordered pairs.
DOMAIN - set of all first coordinate of the ordered pairs in a relation.
RANGE - set of all second coordinate of the ordered pairs in a relation.
Identify the domain and range in the following sets of ordered pairs.
1. {(3,4), (6,11), (13,15), (7,3)}
D: {3, 6, 13, 7}
R: {4, 11, 15, 3}
2. {(47,32),(13, 46),(25, 52)},
D: {47, 13, 25}
R: {32, 46, 52}
Identify if the given examples are relation or not. If yes identify the domain and the
range.
1. {M,A,T,H,E,I,C,S}
2. {(-3,5), (4,12), (5,12), (7,-6)}
3. {2, 4, 6, 8, 10, 12, 14}
4. 2x+y=100, {(45,10),(1, 98),(25, 50)}, is the set of ordered pairs satisfies the given?
Answers:
1. {M,A,T,H,E,I,C,S} > NOT a relation
Why? →Because all the elements inside the set only contains the letters to form
the word MATHEMATICS
2. {(-3,5), (4,12), (5,12), (7,-6)} > Relation
Why? →Because it has the two elements called the domain and range.
D:{-3, 4, 5, 7}
R:{5, 4, 12, -6}
3. {2, 4, 6, 8, 10, 12, 14} > NOT a relation
Why? →Because inside the set there were only random even numbers.
4. 2x+y=100, {(45,10),(1, 98),(25, 50)}, is the set of ordered pairs satisfies the given?
> YES/ Relation
Given : (45,10)
x=45; y=10
2𝑥 + 𝑦 = 100
2ሺ45ሻ + 10
= 100
90 + 10 = 100
𝟏𝟎𝟎 = 𝟏𝟎𝟎
Given : (1,98)
Given : (25,50)
x=1; y=98
x=25; y=50
2𝑥 + 𝑦 = 100
2𝑥 + 𝑦 = 100
2ሺ1ሻ + 98 = 100
2ሺ25ሻ + 50 = 100
2 + 98 = 100
50 + 50 = 100
𝟏𝟎𝟎 = 𝟏𝟎𝟎
𝟏𝟎𝟎 = 𝟏𝟎𝟎
REPRESENTATION OF A RELATION
•
MAPPING DIAGRAM
x
y
Bread
Butter
Ham
Egg
Coffee
Creamer
Champorado
Tuyo
Dinuguan
Puto
•
x
9
y
90
18
81
27
72
36
63
45
54
SET OF ORDERED PAIRS
1. {(Bread, Butter), (Ham, Egg), (Coffee, Creamer), (Champorado, Tuyo), (Dinuguan,
Puto)}
2. {(-1, -2), (-3,-4), (-5,-6), (-7,-8)}
3. {(5,30),(10,40),(15,50),(20,60)}
•
EQUATION
DOMAIN : {-1, -7, 6}
Given the domain solve for the range:
1. y = x+2
Given : x= -1
𝑦 = 𝑥+2
𝑦 = −1 + 2
𝒚 =𝟏
Given : x= -7
Given : x= 6
𝑦 = 𝑥+2
𝑦 = 𝑥+2
𝑦 = −7 + 2
𝒚 = −𝟓
Given : y= -3
𝑥−𝑦 =
𝑥 − ሺ− ሻ =
𝑥+ =
𝑥+ =
𝑥= −
𝑥=
=
=𝟏
𝑦 =
Given : y= 0
𝑥−𝑦 =
𝑥−0=
𝑥=
Given : y= 9
𝑥−9 =
𝑥= +9
𝑥 =15
=
=
=
=𝟓
+2
𝒚 =𝟖
RANGE : {-3, 0, 9}
Given the range solve for the domain:
2. 3x - y=6
Given : y= -3
𝑥−𝑦 =
𝑥 − ሺ− ሻ =
𝑥+
=
𝑥+
=
𝑥=
−
𝑥=
=
Given : y= 0
Given : y= 9
𝑥−𝑦 =
𝑥−9 =
𝑥−0=
𝑥=
𝑥=
𝑥 =15
=
=
=
=𝟓
=𝟏
•
GRAPHING
A = (-2,2)
B = (0,1)
C = (2,0)
+9
A = (-2,2)
B = (0,1)
C = (2,0)
TYPES OF CORRESPONDENCE OF A RELATION
ONE –TO - ONE RELATION
MANY –TO-ONE RELATION
MANY –TO - MANY RELATION
ONE –TO - MANY RELATION