This document discusses relations and different ways to represent them. It defines a relation as any association between elements of one set, and notes that the domain cannot be repeated for it to be a function. It then describes arrow diagrams, tabular methods, and graphical representations as ways to express relations. Arrow diagrams can show one-to-one or many-to-one relations. The document provides examples of these and cautions that the domain must not be repeated for an arrow diagram to represent a function. It also discusses using vertical lines to determine if a graphical representation shows a function.

1. Project
In
Mathematics IV

2. What
is a
Relation?

3. Relation
• It is any association between
elements of one set
• The domain can’t be repeated so
that it can be called a function

4. Different Ways of
Expressing Relation
Arrow Diagram
Tabular Method
Graphical Representation

5. ARROW DIAGRAM
We write the elements from the
domain on one side, and the
elements from the range on the
other, and we draw arrows to show
that an element from the domain is
mapped to the range.

6. ARROW DIAGRAM
kinds of expressing the arrow
diagram.
-One to one
-Many to one

7. ONE TO ONE
Loves
Bryan Zenith
Loves
Paolo Ronalyn

8. ONE TO ONE
In this diagram we illustrate that
Bryan loves Zenith and Paolo loves
Ronalyn.
In the coordinates it can be this:
(Bryan,Zenith) and (Paolo,Ronalyn)
Where Bryan and Paolo are the
domain
while Zenith and Ronalyn are the range.

9. MANY TO ONE
Loves
Bryan Zenith
Loves
Paolo Ronalyn
Arjay Mary

10. MANY TO ONE
In this diagram we illustrate that Bryan
loves Zenith, Paolo loves Ronalyn again. You
noticed that there are new
Characters appeared on the diagram. And that
is Arjay who loves Zenith, and
Mary who loves herself.
So the coordinates are:
(Bryan, Zenith) (Paolo, Ronalyn)
(Arjay, Zenith) (No one, Mary)

11. ARROW DIAGRAM
Reminder!:
In writing an arrow diagram
The x or domain should NOT
Be repeated or else it will not be a
function. While the y or range CAN
be repeated.

12. TABULAR METHOD
It is a set is represented by writing all
the elements of the set, separated by
commas and are enclosed within
brackets { }

13. GRAPHICAL
REPRESENTATION
By showing the relation is by making
a graph.

14. GRAPHICAL
REPRESENTATION
When graphing a point you should know
if that is a function.
-Use the vertical lines that will travel in
the path of the line. If the vertical line
touches another line of the coordinates
that will not be a Function.

15. GRAPHICAL
REPRESENTATION
For Example:

16. GRAPHICAL
REPRESENTATION
You’ve seen that the vertical line
Passed through the line without touches
another line. And can be
called a function

17. EVALUATION
-Just click the letter of the
best answer!
-No returning back!
-Click only the Arrow
button at the right side to
next the slide.

18. EVALUATION
Which of the following is not a way of
expressing a relation?
A. Tabular Method B. Arrow Diagram
C. Table Method D. Graphing Representation

19. CONGRATULATIONS!
Your answer is correct!

20. SORRY!
Your answer is wrong!
Your such a
LOSER!

21. Which of the following are
the kinds of expressing the
Arrow Diagram so that it can
be called a function?
A. (One to One) and (One to many)
B. (One to Many) and (Many to One)
C. (One to One) and (Many to One)
D. (No answer) and (No answer)

22. CONGRATULATIONS!
Your answer is correct!

23. SORRY!
Your answer is wrong!
Your such a
LOSER!

24. Which of the following
relation is not a function?
A.(2,3) and (2,3) B.(3,3) and (2,2)
C.(4,3) and (2,4) D.(5,3) and (15,3)

25. CONGRATULATIONS!
Your answer is correct!

26. SORRY!
Your answer is wrong!
Your such a
LOSER!

27. Which of the following
statements is true about
Relation so that it can be called
a function?
A. Relation is a bond between a repeating
domain and range to be called a
function..
B. Relation is any association between one set
C. Relation is a association between a line
D . No answer

28. CONGRATULATIONS!
Your answer is correct!

29. SORRY!
Your answer is wrong!
Your such a
LOSER!

30. Which of the following
relation is not a function?
A. (Bryan,Zenith) and (Paolo, Ronalyn)
B. (Bryan,Zenith) and (Arjay,Zenith)
C. (Paolo,Mary) and (Bryan,Mary)
D. (Paolo,Mary) and (Paolo,Zenith)

31. CONGRATULATIONS!
Your answer is correct!

32. SORRY!
Your answer is wrong!
Your such a
LOSER!

33. Last and the Hardest
Question:
INSTRUCTIONS:
1. Please CONCENTRATE
2. No turning BACK
3. Don’t be PRESSURED
4. Choose the BEST ANSWER!

34. DO LIKE OUR PRESENTATION?
A. YES
B. NO

35. CONGRATULATIONS!

36. SORRY!

37. THANK YOU!