MATHEMATICS IN THE MODERN WORLD RELATIONS AND FUNCTIONS

2. sontilaer

3. snoitcnuf

4. genar

5. doanim

6. Key words
relations
functions
range
domain

7. Republic of the Philippines
Commission on Higher Education
Region V (Bicol)
LIBON COMMUNITY COLLEGE
Libon, Albay
Leo S. Redita
Presenter
Relations and Functions

8. Objectives
1. Describe and illustrate Rectangular System and its uses;
2. Describe and plot positions on the coordinate plane using the coordinate axes;
3. Define relations and functions;
4. Illustrate a function and a relation in set of ordered pairs, graph of the given
set of ordered pairs, mapping, vertical line test and real-life situation.
5. Determine if the given relation is a function using ordered pairs, graphs and
equations;
6. Describe the domain and range of a function.

9. What is a function?
1
3
2
Essential Questions:
What are the characteristics of a function?
How do you determine if a relation is a function?
How is a function different from a relation?
Why is it important to know which variable is the
independent variable?

10. Definitions
RELATION: A relation is a set of
ordered pairs.
DOMAIN: The domain of a relation
is the set of all inputs.
RANGE: The range of a relation is
the set of all outputs.

11. Definitions
INPUT: Each number in a domain
is an input.
OUTPUT: Each number in a range is
an output.
FUNCTION: A function is a relation with
the property that for each input
there is exactly one output.

12. Definitions
VERTICAL LINE TEST:
The vertical line test says that if
you can find a vertical line passing
through more than one point of a graph
of a relation, then the relation is not a
function. Otherwise, the relation is a
function.

13. Some Definitions
 A relation between two variables x and
y is a set of ordered pairs
 An ordered pair consists of an x and y-
coordinate
 A relation may be viewed as ordered pairs,
mapping design, table, equation, or written
in sentences
 x-values are input, independent
variable, domain.

14. Unit 4 - Relations and Functions
14
Example 1:
What makes this a relation?
{( , ),( , ),( , ),( , ),( , ),( , )}
    
0 5 1 4 2 3 3 2 4 1 5 0
What is the domain?
{0, 1, 2, 3, 4, 5}
What is the range?
{-5, -4, -3, -2, -1, 0}

15. 15
EXAMPLE 1—Identifying the Domain and Range
The relation consists of the ordered pairs
(5,13), (10,25), (15,34), (20,43), and (25,52)
What is the Domain?
{5, 10, 15, 20, 25}
What is the Range?
{13, 25, 34, 43, 52}

16. What is a function?
According to a textbook, “a
function is…a relation in which
every input has exactly one
output”

17. The domain of the relation is the set of
all _____, or _____________.

18. The domain of the relation is the set of
all input, or x-coordinates.

19. The range is the set of all _______, or
_____________.

20. The range is the set of all outputs,
or y-coordinates.

21. EXAMPLE 2—Representing a Relation
Represent a relation (−3, 2), (−2, −2), (1, 1), (1, 3), (2, −3) as
indicated.
List the inputs and the outputs in
order. Draw arrows from the
INPUTS to their OUPUTS.

22. EXAMPLE 2—Representing a Relation
Represent a relation (−3, 2), (−2, −2), (1, 1), (1, 3), (2, −3) as
indicated.
List the inputs and the outputs in
order. Draw arrows from the
INPUTS to their OUPUTS.

23. EXAMPLE 2—Representing a Relation
Represent a relation (−3, 2), (−2, −2), (1, 1), (1, 3), (2, −3) as
indicated.
Graph the ordered pairs as POINTS
in a coordinate plane.

24. EXAMPLE 2—Representing a Relation
Represent a relation (−3, 2), (−2, −2), (1, 1), (1, 3), (2, −3) as
indicated.
Graph the ordered pairs as POINTS
in a coordinate plane.

25. The relations is a function
because
EVERY INPUT IS PAIRED
WITH EXACTLY ONE.
{( , ),( , ),( , ),( , ),( , ),( , )}
    
0 5 1 4 2 3 3 2 4 1 5 0
What is the domain?
{0, 1, 2, 3, 4, 5}
What is the range?
{-5, -4, -3, -2, -1, 0}
EXAMPLE 3—Identifying a Function

26. EXAMPLE 3—Identifying a Function
Represent a relation (−3, 2), (−2, −2), (1, 1), (1, 3), (2, −3) as
indicated.
The relations is a not function
because THE INPUT 1 IS
PAIRED WITH TWO OUTPUTS,
1 AND 3.

27. EXAMPLE 4—Using the Vertical Line Test
In the graph, the vertical
line shown passes through
two points.

28. EXAMPLE 4—Using the Vertical Line Test
In the graph, the vertical line
shown passes through two
points. So, the relation
represented by the graph
IS NOT A FUNCTION .

29. State whether the following relations are functions.
(1, 2), (3, 4), (5, 6), (7, 8)
Function

30. State whether the following relations are functions.
(3, 6), (2, 4), (3, 7), (-7, 9)
Not a Function

31. State whether the following relations are functions.
Not a Function

32. State whether the following relations are functions.
Function

33. Is a relation a function?
•Focus on the x-coordinates, when given a relation
If the set of ordered pairs has different x-coordinates, it ISA function
If the set of ordered pairs has same x- coordinates, it is NOT a function
•Y-coordinates have no bearing in determining functions

34. Which relation mapping represents a
function?
A B

35. Which relation mapping represents a
function?
A B

36. {(– , ),( , ),( , ),( , ),( , ),(– , )}
   
1 7 1 0 2 3 0 8 0 5 2 1
Is this a function?
YES NO

37. Is this a function?
A B