MGMP
SMPK
PENABUR Jakarta
Matematika
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RELATION
and
FUNCTION
MGMP Matematika
SMPK PENABUR Jakarta
Relation & Function
BASIC COMPETENCE:
• Describing and stating relation and function using
representation (sentences, table, graph, diagram & equation)
• Solving problems related to relation and function.
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Notation of Function
Determining f(x)
Given a function:
f ( x ) = 2x
with the domain { 1, 2, 3, 4}
Answer:
x = 1 → f(1) = 2
x = 2 → f(2) = 4
x = 3 → f(3) = 6
x = 4 → f(4) = 8
Then:
Range = { 2,4,6,8 }
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Notation of Function
Example:
Given f : x → 3x + 1
a. Determine f(x).
b. Find the image of -1 on f function.
c. If f (x) = 7, determine x.
d. Determine “The Zero” of the function.
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Notation of Function
Answer:
a) Given: f : x → 3x + 1, then F(x) = 3x + 1
b) The image of -1 on f function:
F(x) = 3x + 1
F(-1) = 3(-1) + 1 = -2
So, the image of -1 on f function is -2.
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Notation of Function
Answer:
c) Given: F(x) = 7, then:
F(x) = 7
7 = 3x + 1
6 = 3x
2=x
So, the value of x is 2.
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Notation of Function
•
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Graph of Function
Given:
f : x → 2x + 1
from domain A = { 0,1,2,3,4,5 }
Draw the mapping graph.
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Graph of Function
1) First Step: Complete the table
x
2x + 1
F(x )
Coordinate
0
2(0) + 1
1
(0,1)
1
2(1) + 1
3
(1,3)
2
2(2) + 1
5
(2,5)
3
2(3) + 1
7
(3,7)
4
2(4) + 1
9
(4,9)
5
2(5) + 1
11
(5,11)
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Graph of Function
2) Second Step: Draw the graph.
The graph of F( x ) = 2x + 1
x-axis for the value of x
y-axis for the value of F(x)
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One to One Correspondence
Two sets, set A and set B, are one to one correspondence if:
• each element of set A has one and only one relation in set B
• each element of set B has one and only one relation in set A.
So, n(A) must be equal to n(B)
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One to One Correspondence
Example :
Given set A and set B with n (A) = n (B) = 3
All possible one to one correspondence that can be made:
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One to One Correspondence
Formula:
n ! = n x ( n – 1 ) x ( n – 2 ) x …. x 1
Example :
Given : A = { 1,2,3 } and B = { a,b,c }
The number of one to one correspondence
n(A) = n(B) = 3, then: 3! = 3 x 2 x 1 = 6
So, there are 6 one to one correspondence that can be made.
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THANK YOU
MGMP Matematika SMP PENABUR Jakarta