The document defines relational functions and provides examples. It discusses: 1) The definition of a relation as a set of ordered pairs, with the domain as the set of inputs and range as the set of outputs. 2) Examples of relations and their domains and ranges. 3) The definition of a function as a relation where each input is paired with exactly one output. 4) Examples and operations involving relational functions, including composite functions.

1. RELASI FUNGSI
Oleh : ISNAINI FAHMI, S.Pd
UPTD SMA NEGERI 9 TANGERANG
Jl. H. Jali No. 9 Kelurahan Kunciran Jaya Kecamatan Pinang
Kota Tangerang

2. Definisi
Relation  A set of ordered pairs.
Domain  The set of all inputs (x-values)
of a relation.
Range  The set of all outputs (y-values)
of a relation.

3. Contoh 1
Relation  { (-4, 3), (-1, 7), (0, 3), (2, 5)}
Domain  { -4, -1, 0, 2 }
Range  { 3, 7, 5 }

4. Contoh 2
Relation 
{ (-2, 2), (5, 17), (3, 3), (5, 1), (1, 1), (7, 2) }
Domain  { -2, 5, 3, 1, 7 }
Range  { 2, 17, 3, 1 }

5. Contoh 3
Relation  y = 3x + 2
Domain  {x: x Є R }
Range  {y: y Є R }

6. Contoh 4
1
5
7
-1
0
2
11
Relasi  {(1, 0), (5, 2), (7, 2), (-1, 11)}
Domain  {1, 5, 7, -1}
Range  {0, 2, 11}

7. Definisi
Function  A relation in which each
element of the domain ( x value) is
paired with exactly one element of the
range (y value).

8. Manakah Yang termasuk
Fungsi ?
{ (0, 2), (1, 0), (2, 6), (8, 12) }
{ (0, 2), (1, 0), (2, 6), (8, 12), (9, 6) }
{ (3, 2), (1, 0), (2, 6), (8, 12), (3, 5), }
{ (3, 2), (1, 2), (2, 2), (8, 2), (7, 2) }
{ (1, 1), (1, 2), (1, 5), (1, -3), (1, -5) }

9. Operasi Fungsi
g(x) = 3x + 2
f(x) = x2 + 2x + 1
f(x) + g(x) =
f(x) - g(x) =
f(x) • g(x) =
x2 + 2x + 1 + 3x + 2
(x2 + 2x + 1) - (3x + 2)
= x2 + 5x + 3
= x2 - x - 1
(x2 + 2x + 1) • (3x + 2)
= 3x3 + 2x2 + 6x2 + 4x + 3x + 2
= 3x3 + 8x2 + 7x + 2
f(x) ÷ g(x) =
(x2 + 2x + 1)
(3x + 2)
Domain?
 
3
2
,
: 

 x
R
x
x
 
R
x
x 
:
 
R
x
x 
:
 
R
x
x 
:

10. Fungsi Komposit
g(x) = 3x + 2
f(x) = x2 + 2x + 1
f(g(x)) =
g(f(x)) =
= (3x+2)2 + 2(3x+2) + 1
= 3(x2 + 2x + 1) + 2
= 9x2 + 12x + 4 + 6x + 4 + 1
= 3x2 + 6x + 3 + 2
Domain?
 
R
x
x 
:
 
R
x
x 
:
f(3x+2)
= 9x2 + 18x + 9
g(x2 + 2x + 1)
= 3x2 + 6x + 5

11. Fungsi Komposit
g(x) = x - 3
f(x) = x2 - 4x + 5
f(g(x)) =
g(f(x)) =
= (x-3)2 - 4(x-3) + 5
= (x2 - 4x + 5) - 3
= x2 - 6x + 9 - 4x + 12 + 5
= x2 - 4x + 5 - 3
Domain?
 
R
x
x 
:
 
R
x
x 
:
f(x-3)
= x2 - 10x + 26
g(x2 - 4x + 5)
= x2 - 4x + 2

12. f(x) = x2 + 3x + 5
f(g(x)) =
= ( )2 + 3( ) + 5
=
Domain?
 


,
3
f( )
=
3
)
( 
 x
x
g
3

x
3

x 3

x
5
3
3
3 


 x
x
3
3
2 

 x
x
x – 3 > 0
x > 3
Fungsi Komposit

13. Fungsi Komposit
f(x) = x2 + 3x + 5
g(f(x)) =
=
= x2 + 3x + 5 - 3
Domain?
g(x2 + 3x + 5)
=
3
)
( 
 x
x
g
  3

2
3
2

 x
x
   





 ,
2
3
, 
x2 + 3x + 2 > 0
(x + 2)(x + 3) > 0
-2
-3
x2 + 3x + 5