function

1. Four Pics one word

2. Four Pics one word

4. 1. Domain is the set of all x or input values.
Reveal
Answer
YES NO
2.
Set is a collection of well-defined and distinct objects, called
elements that share a common characteristics.
3. Range is the set of all x input values.
4. Ordered pair is a pair of objects taken in a specific order.

5. 5
Relation is a rule that relates values from a set of values
(domain) to a second set of values (range).
Reveal
Answer
YES NO
6.
In the given relation, the domain value 0 corresponds to the
range value -2? {(-1,2), (-2,4), (2,5), (0,-2), (2,0)}.
7. {(0,2), (1,3), (4,3), (1,2)}, is an example of a function.

6. What do you need to know?
1 determine functions and relations;
2
illustrate functions through mapping diagram, sets
and graphs; and
3 represent real-life situations using functions.

7. Ordered pair
An ordered pair is a composition of the x coordinate (abscissa) and the y
coordinate (ordinate), having two values written in a fixed order within
parentheses.
(1,2)
𝒙 − 𝒄𝒐𝒐𝒓𝒅𝒊𝒏𝒂𝒕𝒆 𝒚 − 𝒄𝒐𝒐𝒓𝒅𝒊𝒏𝒂𝒕𝒆

8. Sets
A set is a collection of objects, called the
elements or members of the set.
1 2
3
6
4 5
1,2,3,4,5,6 𝑎, 𝑏, 𝑑, 𝑒, 𝑓, 𝑔
b d
e
g
a f

9. What is relation?
A relation is a set of ordered pairs. If you limit it to
points in the Cartesian Plane, it is a set of ordered pairs
(𝑥, 𝑦) such that 𝑥 and 𝑦 belongs to the set of real
numbers 𝑅.

10. Example
{ 𝟏, −𝟏 , 𝟐, −𝟑 , 𝟎, 𝟓 , −𝟏, 𝟑 , 𝟒, −𝟓 , −𝟏, 𝟓 , 𝟒, −𝟒 }
Domain (x) is the set of all first coordinates.
Range (y) is the set of all second coordinates.
Domain
Range
{-1,0,1,2,4}
{-5,-4, -3, -1,3, 5}

11. Representation of relation
Example: { 𝟏, 𝟏 , (2,3), (3,4) ,(𝟒, 𝟓)
Table of Values
X Y
1 1
2 3
3 4
4 5
1
2
3
4
1
3
4
5
X Y
Mapping Graphing

12. Types of relation
1
2
3
4
1
3
4
5
X Y
One – to – One
Relation
1
5
1
3
4
5
X Y
One – to – Many
Relation
1
2
3
4
1
X Y
Many-to -one
Relation

13. What is function?
𝑦
𝑥
𝑥
𝑥
𝑥
𝒚 = 𝒙𝟐
X 𝒚 = 𝒙𝟐
1 (𝟏)𝟐= 𝟏
2 (𝟐)𝟐
= 𝟒
3 (𝟑)𝟐
= 𝟗
4 (𝟒)𝟐
= 𝟏𝟔
𝒚 = 𝒇 𝒙 = 𝒙𝟐
𝒚 = 𝒇 𝒙
𝐷𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 𝑠𝑒𝑡
𝑛𝑎𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛
𝐼𝑛𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 𝑠𝑒𝑡

14. What is function?
𝒙
𝒚
Independent set
Dependent set

15. What is function?
A function is a set of ordered pairs in which
no two ordered pairs have the same first
component but different second components.

16. Example
3
6
9
12
15
4
8
12
16
X Y
Not a function
1
2
3
4
1
X Y
Function
1
2
3
4
1
3
4
5
X Y
Function

17. Example
 Functions as a set of ordered pairs  Functions as equations
 Functions as graphs  Functions as table of values
𝐹 = { 1,1 , 3,5 , 4,6 , 8,9
𝐺 = { 1,0 , 2,0 , −1,5
𝑓 𝑥 = 𝑥2 + 1
𝑔 𝑥 = 4 − 5𝑥

18. Vertical l I ne test
The vertical line test is a graphical method of
determining whether a curve in the plane
represents the graph of a function by visually
examining the number of intersections of the
curve with vertical lines.

19. Examples

20. Examples

21. Examples

22. Relatio
n
Function
Note: All functions are relations, but not all relations are functions.

23. Function limitation
Input Output
x 𝒚 = ± 𝒙
4 ±2
9 ±3
16 ±4
25 ±5
𝒚𝟐=x
Not a function
𝒚 = ± 𝒙

24. Application in real life
 Water bill depends on water consumption.
 Speed is a function of time and distance travelled.
 Revenue is based on the price and the number of products sold.
 A vending machined – A soda, snack, or stamp machine the user puts in money,
punches specific button, and a specific item drops into the output slot.

25. Application
1. Let 𝑅 = { 1,2 , 3,4 , 5,11 , 3,1 . Find the domain and range of the given relation.
2. In everyday life, you encounter many relations which may or may not represent a functions.
Which of the following everyday relations are functions.
a. 𝑥 is a daughter of 𝑦 (𝑥 and y are women).
b. 𝑥 is taller that 𝑦 (𝑥 and 𝑦 are residents of the Philippines)
c. 𝑥 has received a dental treatment from 𝑦 (𝑥 and 𝑦 are professionals)
d. 𝑥 is a digit (0,9) on a telephone dial pad and 𝑦 is a corresponding letter.
3. Find the function value given the particular values of 𝑥.
a. 𝑓 𝑥 = 2𝑥 − 11; 𝑓 1
b. 𝑔 𝑥 = 2𝑥2 − 7; 𝑔(−2)

26. Assignment
Please study the operations in function. In a short bond
paper write the five operations on functions and give
one example with complete solution.