ma thematic presentation chapter relation and function
Post on 10-Apr-2018
218 Views
Preview:
TRANSCRIPT
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
1/44
Relation And Function
Annisa Fitriana (8 SBI B/2)
Dzaky El Fikri (8 SBI B/12)
Askari Ishmat (8 SBI B/17)
Wahyu Nugroho (8 SBI B/18)
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
2/44
Domain and range, relations andfunctions
Relation:A rule for pairing the elements of set a withthe element of set b.
{(3,2),(1,5),(0, 2)}
Domain: all of the first coordinates of a relation (thinkof the domain as the inputs).
3,1,0
Range: all of the 2nd coordinates of a relation (thinkof the range as the outputs).
2, 5, 2
Function: a relation in which each element of the
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
3/44
{(2,3),(-1,5),(4,-2),(9,9),(0,6)} This is arelation
The domain is the set of all x values in the relation
{(2,3),(-1,5),(4,-2),(9,9),(0,6)}
The range is the set of all y values in the relation
{(2,3),(-1,5),(4,-2),(9,9),(0,6)}
domain = {-1,0,2,4,9}
These are example of the x values written in a set from
smallest to largest
range = {-6,-2,3,5,9}
These are the y values written in a set from smallest to
largest
DOMAIN AND RANGE
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
4/44
Domain (set of all xs) Range (set of all ys)
1
2
3
4
5
2
10
8
6
4
A relation assigns the xs with ys
This relation can be written {(1,6),(2,2),(3,4),(4,8),(5,10)}
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
5/44
Ow now I know
about Function
Set A is the domain
1
2
3
4
5
Set B is the range
2
10
86
4
Must use all the xs
A function f from set A to set B is a rule of correspondence that assigns to each element
x in the set A exactly one element y in the set B.
The x value can only be assigned to one y
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
6/44
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
7/44
Menu
Understanding relation. Arrow diagram.
Cartesian diagram.
Set of ordered pairs.
Function.
Notation.
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
8/44
Understanding Relation
Relation from set A to set B is defined as a connector to pair themembers of set A to the members of set B.
For example, set A {Konci, Reza, Nosa} can be connected to setB {Ahmad, Aji, Heri} by relation son of.
Relations can be expressed by 3 ways, arrow diagram,Cartesian diagram, and set of ordered pairs.
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
9/44
ArrowDiagram
Arrow diagram uses 2 sides to displays the members of set Aand set B.
These members of 2 sets are connected each other by arrows,
and these arrows represents the relation of both sets.
The relation is written between the set names.
Format
Example
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
10/44
ArrowDiagram Format
AA BBRelationRelation
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
11/44
Konci
Reza
Nosa
Example of ArrowDiagram
Aji
Ahmad
Heri
AA BBis the son ofis the son of
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
12/44
CartesianDiagram
This diagram is usually used in determiningcoordinates, but also useful for expressing relation.
This diagram uses 2 axis's, x axis and y axis. X axis
usually used for domain, and y axis for codomain.
Example
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
13/44
CartesianDiagram Example
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
14/44
Set ofOrdered Pairs
It is used by listing a member and its pair in a bracket. For example: {(Konci, Ahmad), (Nosa, Heri), (Reza,
Aji)}.
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
15/44
Function
For example, set A contains name of boys (Nosa, Suluh, Konci,Reza), and set B contains name of biologist fathers (Heri, Budi,
Aji, and Akhmad).
Because that, we can build a relation between two sets whichevery element of set A always have exactly one pair in set B,
because a child can only able to have one biologist father.T
hisspecial kind of relation is called Function.
Function is special relation while the members in domain hasexactly one pair in codomain.
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
16/44
Terms in Function
Domain:The first region in function. All of the memberof set in this region must have exactly one pair in
codomain to be a function.
Codomain:The region of pair set of domain.
Range:The region of members of pair set of domain.
Range is always become region of codomain, but
codomain isnt always become region ofRange.
To count possible ways of function of both sets,
n(codomain)n(domain)
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
17/44
Notation of Function
Notation of function is a notation that represents therelation of that both sets including the characteristicof that set.
If the members of domain set is called x, the notationof members of domain set is called f(x).
If the function from domain set to codomain set isless 1 than, we can write the notation of functionf(x)=x+1
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
18/44
One toOneCorrespondence
A set is said to have A one to one correspondence with set B
if every element of A is paired with exactly one element of B
and every element of set B is paired with exactly one
element of A.T
herefore the number of elements of the set Aand B must be equal
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
19/44
Function Formula
Formulating function
It is common to introduce a function which follow a certain
rules with a name such as f , g , h or any other lower case
Latin letters
A mapping by a function f hat map ever element x of set A to
element y of set B can be denoted
the notation f : x y is read function f maps x to y there y
is called the image (map) of x under y
F : x y
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
20/44
Figure below shows a function f mappng A to B if x is an
elements of the doain of A then the image of x under f is
denoted by f(x) and is read a function of x
Example given the mapping f : x x + 2
Since the image of x under f can be denoted by f(x) we can
express the mapping as f(x) = x + 2
The form f(x) = x + 2 is called a function formula
x F(x)
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
21/44
Number Possible Ways
ofOne toOne
Correspondence
A = { a , b , c } B = { 1 , 2 , 3 }
To find how many possible ways one to one correspondence
set A to set B
N(A) = N(B) = 3!(three factorial)
= 3.2.1 = 6 possible ways
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
22/44
We commonly call functions by letters. Because function starts with f, it is a commonlyused letter to refer to functions.
632 2 ! xxxf
The left hand side of this equation is the function notation. It tells us two things. We
called the function f and the variable in the function is x.
This means the
right hand side
is a function
called f This means the
right hand side has
the variable x in it
The left side DOES NOT MEAN f
times x like parenthesis usually do, it
simply tells us what is on the right
hand side.
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
23/44
632 2 ! xxxf
So we have a function called f that has the variable x in it.
Using function notation we could then ask the following:
623222 2 !f
8668623422 !!!f
Dont forget order of operations---powers, then multiplication, finally
addition & subtraction
f(2). This means to find the function f and instead of having an x in it,put a 2 in it. So lets take the function above and make parenthesis
everywhere the x was and in its place, put in a 2.
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
24/44
6322
!
xxxf
Example f(-2).
623222 2 !f
20668623422 !!!fExample f(3). 632 2 ! xxxf
633323 2 !f
362718693923 !!!f
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
25/44
532 ! xxxf
55355 2 !f
4551525653255 !!!f
Example f(5).
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
26/44
63 ! xxfThis means the
right hand side
is a function
called f This means the
right hand side has
the variable x in it,
If the variable x
change like x+3 orx+4 the right side
also change the
variable x with the
command.
If the variable change
This x has to be
changed into thevalue of x in the left
example: in the left
show x+3, we have
to changed this x
into the x+3 to.
Untuk hasil
perubahan
fungsi adalah
dengan
mengurangkan
hasil fungsi
dengan f(x)
contoh:
f(x+3)-f(x)= 15
The first step find th
result of f(x+3)
The second
subtract the result
of f(x+3) with f(x)
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
27/44
53 ! xxf
5333 ! xxf
1435933 !! xxxf
Example f(x+3).
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
28/44
4! xxf
444 ! xxf
8444 !! xxxf
Example f(x+4).
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
29/44
4! xxf
41515 ! xxf
5541515 !! xxxf
Example f(5x+1).
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
30/44
4! xxf
41515 ! xxf
5541515 !! xxxf
Example f(5x+1).
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
31/44
4! xxf
5)1(21 ! xxf
5)1(21 ! xxf
Example f(x+1).
725221 !! xxxf
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
32/44
f(x+1)-f(x)= 12
The first step findthe result of f(x+1)
and the f(x) is 2x+5.
The second
subtract the result
of f(x+3) with f(x)
To know the change result of he f(x)
we subtract the result of the function
with f(x) example
52 ! xxf
5)1(21 ! xxf
5)1(21 ! xxf
725221 !! xxxf
5272)()3( ! xxxfxf
125722)()3( !! xxxfxf
12)()3( ! xfxf12 is the value of the change of
function
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
33/44
5! xxf
533 ! xxf
8533 !! xxxf
Example f(x+3).
13 is the value of the change of
function
58)3( ! xxxfxf
the value of the change of function
1358)3( !! xxxfxf
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
34/44
7! xxf
744 ! xxf
11744 !! xxxf
Example f(x+4).
18 is the value of the change of
function
711)3( ! xxxfxf
the value of the change of function
18711)3( !! xxxfxf
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
35/44
4! xxf
433 ! xxf
7433 !! xxxf
Example f(x+3).
12 is the value of the change of
function
48)3( ! xxxfxf
the value of the change of function
1257)3( !! xxxfxf
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
36/44
One to one correspondence
The sum of element of set A and B must same.
A set A is said to have a one to one correspondence
with set b if every element of set A is paired with
exactly one element of A, therefore the number
element of set a and must be equal Number possible way of the one to one
correspondence:
Using factorial number(!)
Example: A={a,b,c} B={1,2,3}. Answer: 3!=3.2.1=66 is the number possible of the one to one correspondence
between set A to set B
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
37/44
Function Graph
Graph of function is special relation from set A to set
B in form of graph.The form of graph is Cartesian
Diagram.
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
38/44
How to make Function Graph
First we make table like this :
And Finally make the Cartesian Diagram from the table
x
f(x)
x,f(x)
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
39/44
Example of Function Graph
f (x) = x + 5
x = {1,2,3,4,5)
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
40/44
Example of Function Graph
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
41/44
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
42/44
Table
x
f(x)
x,f(x)
1 2 3 4 5
109876
(1,6) (2,7) (3,8) (4,9) (5,10)
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
43/44
CartesianDiagram
1 4 532
6
10
9
8
7
-
8/8/2019 Ma Thematic Presentation Chapter Relation and Function
44/44
top related