Embed Size (px)
Citation preview
RIGEN V. MAALAM BSED-Math 3
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.
Click icon to add picture
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
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:
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
A function is a relation in which each element in the domain corresponds to exactly one or unique element in the range.
DEFINITION:
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
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
Methods of Describing 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
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
(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)
(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
(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
Click icon to add picture
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
Click icon to add picture
f(x)=-x+1 f(x)=x2-2 f(x)=x3+1
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.
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
Click icon to add picture
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:
