Powerpoint for Relation and Function

1. By Ms. Angelika Cruz
GOOD
AFTERNOON
CLAS
S!

2. RECALL

3. ICE
BREAKER

4. GROUP ME!
Group the following objects in such a way that
they have a common properties/characteristics
Direction:
red
adobo
orange
berry
pink
pizza
yellow
banana
spaghetti
white
mango
french
fries
apple
carbonara
grapes

5. GROUP ME!
Group the following objects in such a way that they
have a common properties/characteristics
Direction:
FOOD FRUIT COLOR

6. GROUP ME!
Group the following objects in such a way that they
have a common properties/characteristics
Direction:
FOOD FRUIT COLOR
red
yellow
orange
pink
white
mango
banana
apple
berry
grapes
pizza
adobo
french
fries
spaghetti
carbonara

7. GROUP
ACTIVITY

8. How many elements are there in the given set
of ordered pairs
What elements belong to the first set? What
elements belong to the second set?
How do we illustrate/represent the set of
ordered pairs?

9. RELATIO
NS AND
FUNCTIO
NS

10. OBJECTIVES
At the end of the lesson, the student must be able to:
a. illustrate a relation and a function.

11. • A set of ordered pairs.
• It is represented as (x,
y) where x is the
abscissas or domain of
the relation and y is the
ordinate or range of
the relation.
RELATIONS
Example:
{(1, 1), ( 2, 3), (3, 4)}
Domain (x) = {1 , 2, 3}
Range (y) = {1, 3, 4}

12. RELATIONS
Is {(1,2), (2,3), (3,4), (4,5)} a
relation?
Is {(1,2,3,4,5)} a relation?
Is {(1,2), (4,5,6)} a relation?
YES
NO
NO

13. TABLE OF VALUES MAPPING
DIAGRAM
GRAPH RULE OR
EQUATION
REPRESENTATI
ON
OF RELATIONS

14. REPRESENTATION OF
RELATIONS
TABLE OF VALUES
• It is a list of numbers that is used to
substitute one variable to find the value of
the other variable within the given equation.
{(red, color), (pizza, food), (grapes, fruit),
(Sheena, BINI), (Jm, Fyang)}

15. REPRESENTATION OF
RELATIONS
TABLE OF VALUES
x
y
red
color
pizza
food
grapes
fruit
Sheena
BINI
JM
Fyang
a. Horizontal b. Vertical
x y
red color
pizza food
grapes fruit
Sheena BINI
JM Fyang

16. REPRESENTATION OF
RELATIONS
MAPPING DIAGRAM
• It consists of two columns where a pair is
connected by a line.
• It can be rectangular or circular shape
{(red, color), (pizza, food), (grapes, fruit),
(Sheena, BINI), (Jm, Fyang)}

17. REPRESENTATION OF
RELATIONS
x
red
pizza
grapes
Sheena
JM
y
color
food
fruit
BINI
Fyang
MAPPING DIAGRAM
a. Rectangular b. Circular
red
pizza
grapes
Sheena
JM
color
food
fruit
BINI
Fyang
x y

18. REPRESENTATION OF
RELATIONS
MAPPING DIAGRAM
FOUR DIFFERENT CORRESPONDENCE

19. REPRESENTATION OF
RELATIONS
MAPPING DIAGRAM
FOUR DIFFERENT CORRESPONDENCE

20. REPRESENTATION OF
RELATIONS
GRAPH
• It describes a
relationship between
points and lines. The
graph consists of some
points and lines. It
illustrates the
relationship of the
values of x and y.
{(0, 8), (1, 7), (2, 6), (3, 5), (4,
4)}

21. • A set of ordered pairs is
a function if there is no
repetition in the
domain(x)
• It is a relation in which
every element in the
domain(x) is mapped to
exactly one element in
FUNCTIONS
Example:
{(1, 1), ( 2, 3), (3, 4)}
Domain (x) = {1 , 2, 3}
Range (y) = {1, 3, 4}
It is a FUNCTION.

22. REPRESENTATION OF
RELATIONS
RULE OR EQUATION
• It shows how one
variable depends on the
other variable. It also
shows how the value of y
depends on the value of
x.
{(0, 8), (1, 7), (2, 6), (3, 5), (4,
4)}
x + y = 8
y = -x + 8 or x = -y +
8
x
y
0
8
1
7
2
6
3
5
4
4

23. FUNCTIONS
Is {(0,2), (-1,3), (-2,4)} a function?
Is {(-2,2), (-2,3), (-2,4)} a function?
Is y = 2x - 1 a function?
YES
NO
YES

24. FUNCTIONS
Is it a function or not?
Is y² = x + 1 a function?
YES
NO
x
y
1
2
2
5
3
8
4
11

25. NOTE
• All functions are relations but
not all relations are functions.
• Among the four correspondence
for relations, only one-to-one
correspondence and many-to-one
correspondence can be classified
as functions.

26. FUNCTIONS
VERTICAL LINE TEST
A graph represents a function if and only
if a vertical line intersects the graph at
exactly one point.
x
y y
x

27. I HAVE
WAYS!
Answer the following in the Manila Paper and
choose three representative to present your
work.
Direction
:

28. I HAVE
WAYS!
A. Given the graph below,
show the relation as;
1. Table of Values
2. Mapping Diagram
3. Set of Ordered Pairs

29. B. Illustrate the relation described by the rule y = 2x -1
using a table of values, set of ordered pairs and
mapping diagram.
x
y
2 3 4 5
1.Given the values of x. Substitute it to the given rule to
determine the y- value.
2.Write the ordered pairs in a set. You can refer to the table
above.
3.Draw the mapping diagram by grouping the x values and y
values and put an arrow line to connect the ordered pairs.

30. SEATWORK
# 4
ILLUSTRATING RELATION AND FUNCTION

32. ASSIGNMEN
T
Direction: Given the rule , complete the table of values and
determine whether it is a function or mere relation. An
example is provided for each item.
1. Equation: y = 3x - 2
Solution: x = -2
y = 3(-2) - 2
y = (-6) - 2
y = -8
The equation y = 3x - 2 represents a ___________.

33. ASSIGNMEN
T
2. Equation: y² + x = 2
Solution: x = -2
y² -2 = 2
y² = 2 + 2
y² = 4
√y² = ± 4
√
y = ± 2
The equation y² + x = 2 represents a ___________.
Direction: Given the rule , complete the table of values and
determine whether it is a function or mere relation. An
example is provided for each item.

34. ASSIGNMEN
T
3. Equation: y = 2x² + 3x - 1
x = -2
y = 2(-2)² + 3(-2) - 1
y = 8 + (- 6) - 1
y = 1
The equation y² + x = 2 represents a __________.
Direction: Given the rule , complete the table of values and
determine whether it is a function or mere relation. An
example is provided for each item.

35. THANK
YOU!
By Ms. Angelika Cruz