The document discusses relations and functions. It defines a relation as a set of ordered pairs where the first element is from one set and the second is from another. A function is a special type of relation where each element of the first set is paired with exactly one element of the second set. It provides examples to illustrate relations, functions, and how to identify the domain, codomain, and range of a function based on an arrow diagram.

1. ARE YOU READY TO STUDY TODAY ??
COME ON WE SAY : “ CHEER UP “

2. FUNCTIONS, EQUATIONS
AND QUADRATIC
INEQUALITIES
DIAH PERMATASARI

3. RELATION and function

4. 1. Explanation Relation & Function
Sequence couple & Cartesius
product
Relation function

5. Definition
Number Pair (x, y) with x is first order and y is second order then
said Sequence couple
Example 2.1 :
Point A (2,3) is value absis x = 2, ordinat y = 3
Point A (2,3) different with point B(3,2)
If A and B is two compilation a not empty, then Cartesius product
compilation A and B is all compilation sequence couple (x,y) with x ϵ A
and y ϵ B. write :
A x B = {(x,y) | x ϵ A and y ϵ B}
For Example 2.2 :
A = {4,5,6} and B= {0,2}, definite :
a. A x B b. B x A
Answer : a. A x B = {(4,0),(4,2),(5,0),(5,2),(6,0),(6,2)}
b. B x A = {(0,4), (0,5),(0,6),(2,4),(2,5),(2,6)}

6. Definition
For example A x B is Cartesius product compilation A and B, then
relation R from A to B is compilation of any kind part for Cartesius
product A x B.
Example 2.3 :
Back Attention example 2.2 . A = {4,5,6} and B= {0,2},
The Cartesius product A x B can be found some component
compilation for A x B is :
a. R1 = {(4,0),(5,0),(5,2),(6,2)}
b. R2 = {(4,0),(4,2),(5,0),(5,2),(6,0)}
c. R3 ={(4,0),(5,0),(6,0)}
4
0
5
6 2

7. Compilation-compilation R1, R2, and R3 is part compilation for
cartesius product A x B is a familiar as relation for compilation A
to compiltion B.
From on explanation, the relation R = {(x ,y) | x ϵ A and y ϵ B}
can be matter that is
a. Compilation first ordinat ( absis) from sequence couple (x,y)
that is origin area (domain ) relation R
b. Compilation B that is companion area (kodomain) relation
R.
c. Part Compilation from B with x R y or y ϵ B that is output
area (range) relation R.

8. Definition
Relation from compilation A to compilation B that is
function or cartography, if each element
(component) on compilation A exact form a pair only
with a element (component ) on compilation B.
For example f is a function or cartography from
compilation A to compilation B, then function f can be
symbol with
f :A→B

9. 0
0 Picture 2.3. The
0 function f can be write
0 that is f : x → y = f (x)
0
For example, x ϵ A, y ϵ B that (x,y) ϵ f , then y is chart or imagination from x
by function f. the chart or imagination can be said with y = f(x), you can see a
picture 2.3. So, the function f can be write that is
f : x → y = f (x)
for example, f : A → B, then
a. Origin area (domain) function f is compilation A and the symbol with Df
b. Companion area (kondomain) function f is compilation B and the
symbol with Kf , and
c. Output area (Range) function f is compilation from all chart A in B and
the symbol with Rf.

10. Example
1. What is a diagram a function or not, and give reason ?
F H
A A B
B
a a
k k
b b
l l
c c
m m
d d

11. Answer :
a. Relation F is function because every component compilation
A connection with exact one component compilation B.
b. Relation H isn’t function because be found one component
compilation A, that c isn’t use companion in B
2. Definite domain, kodomain, and range from function f the
indication by bow and arrow diagram ? F
A B
Answer :
a. Compilation A = {a,b,c,d} is origin area or a.
>
domain from f is Df = {a,b,c,d} .4
b. .5
b. Compilation B = {4,5,6,7,8} is companion >
.6
area or kodomain from function f, is Kf = c. .7
{4,5,6,7,8} .8
d.
c. Range or output area from function f is Rf
= {4,5,6}