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RIGEN V. MAALAM BSED-Math 3 Relations and Functions

Relations and Functions

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Page 1: Relations and Functions

RIGEN V. MAALAM BSED-Math 3

Relations and Functions

Page 2: Relations and Functions

Learning Objectives:a. Distinguish function from mere relations.b. Describe functions using different methods.c. Discuss the importance of building a strong and positive relationship with the people around you.

Page 3: Relations and Functions

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RELATIONS

START TIME 1:00 pm2:00 pm7:00 pm

Set A

ATHLETIC EVENT

 

FootballVolleyball

ChessBasketball

Set B

Figure 1

STUDENTS 

AngelieCarme

ChristianMaritesNicholeEddieChary

Set A

SECTION 123  

Set B

Figure 2

Page 4: Relations and Functions

A relation is a correspondence between two sets where each element in the first set, called the domain, corresponds to at least one element in the second set, called the range.

DEFINITION:

Page 5: Relations and Functions

Mere Relation

Function

START TIME 1:00 pm2:00 pm7:00 pm

Set A

ATHLETIC EVENT

 

FootballVolleyball

ChessBasketball

Set B

Figure 1STUDENTS

 

AngelieCarme

ChristianMaritesNicholeEddieChary

Set A

SECTION 123  

Set B

Figure 2

Click icon to add pictureRELATIONS

Page 6: Relations and Functions

A function is a relation in which each element in the domain corresponds to exactly one or unique element in the range.

DEFINITION:

Page 7: Relations and Functions

Characteristics of Functions

SUBJECTS 

TrigonometryAlgebra

ChemistryGeometryPhysics

Domain

CALL NO. 510512513516530

Range

Figure 3

APPLIANCE 

Turbo BoilerMicrowave Oven

RefrigeratorWashing Machine

TV Set 

Domain

SALE PRICE P8, 000P12, 000P14, 000P16, 000P18, 000  

Range

Figure 4

Page 8: Relations and Functions

Main characteristics of a function:

1. Each element in the domain is matched with exactly one, unique element in the range.

2. Two or more elements in the domain may be matched with the same element in the range.

3. Some elements in the range may not be matched with any element in the domain.

REMEMBER

Page 9: Relations and Functions

Methods of Describing Functions

Page 10: Relations and Functions

Characteristics of Functions

SUBJECTS 

TrigonometryAlgebra

ChemistryGeometryPhysics

Domain

CALL NO. 510512513516530

Range

Figure 3

APPLIANCE 

Turbo BoilerMicrowave Oven

RefrigeratorWashing Machine

TV Set 

Domain

SALE PRICE P8, 000P12, 000P14, 000P16, 000P18, 000  

Range

Figure 4

Page 11: Relations and Functions

A school canteen sells lunch for P45. To facilitate the payments and avoid inaccuracy in computation, the student manager prepared a table to which she can refer when receiving payments.Number

of Students

(x)1 2 3 4 5 6 7 8

Amount Due (y) 45 90 135 190 225 270 315 360

B. Table of Values

Page 12: Relations and Functions

(1, 45), (2,90), (3,135), (4,190),…

Number of

Students (x)

1 2 3 4 5 6 7 8

Amount Due (y) 45 90 135 190 225 270 315 360

C. Ordered Pairs

(number of students, amount due)

General Rule:(x,y)

Page 13: Relations and Functions

(1, 45), (2,90), (3,135), (4,180),…(x,y)

D. Equation

45=45(1)

90=45(2)

135=45(3)

180=45(4)

General Rule:

y=45x or

f(x)=45x

Page 14: Relations and Functions

(x,y)

(1, 45), (2,90),

(3,135), (4,180)

E. Graph

f(x)=45x0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

50

100

150

200

250

Number of Students

Am

ount

Due

Page 15: Relations and Functions

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To sketch the graph of a function, set the ordered pairs in a table, plot the points in the coordinate plane and connect them, with a smooth curve if necessary. Then, name the graph.

REMEMBER

Page 16: Relations and Functions

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f(x)=-x+1 f(x)=x2-2 f(x)=x3+1

Page 17: Relations and Functions

  A set of points in a coordinate plane is the graph of a function if and only if no vertical line intersects the graph at more than one point. If any x-value corresponds to more than one y-value, then y is not a function of x.

REMEMBER

This graph is not a graph of a function.

Page 18: Relations and Functions

Click icon to add pictureDetermine whether each of the following describes a function or a mere relation. Give reasons for your answers.

ACTIVITY:

567

aeiou

567

aeiou

1. 2.3.

4. 5.

2,4,6,8

,3,5,7,9

A

B

. 2,3 , 4,5 , 6,7 , 8,9

. 2,1 , 2,3 , 4,7 , 6,9

. 2,1 , 4,3 , 6,5 , 8,5

a

b

c

Page 19: Relations and Functions

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In a short bond paper, make a 2-paragraph reflection paper of what you have learned in this topic and which part of the lesson you find difficulty in understanding. Pass it on Thursday, November 12, 2015.

ASSIGNMENT: