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DIAH PERMATASARI

FUNCTIONS, EQUATIONS AND

QUADRATIC INEQUALITIES

RELATION and function

1. Explanation Relation & Function

Sequence couple & Cartesius product

Relation function

DefinitionNumber 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 = 3Point 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 AAnswer : 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)}

DefinitionFor 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)}

0

2

4

5

6

From on explanation, the relation R = {(x ,y) | x ϵ A and y ϵ B} can be matter that isa. Compilation first ordinat ( absis) from sequence couple (x,y)

that is origin area (domain ) relation Rb. 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.

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.

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

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)

Picture 2.3. The function f can be

write that is f : x → y = f (x)

0

0

0

0

0

for example, f : A → B, thena. 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.

Example1. What is a diagram a function or not, and give reason ?

a

b

c

d

k

l

m

A A

a

b

c

d

k

l

m

BBF H

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 ?

a .

b .

c .

d.

. 4. 5. 6. 7. 8

A BF

Answer :a. Compilation A = {a,b,c,d} is origin area or

domain from f is Df = {a,b,c,d}b. Compilation B = {4,5,6,7,8} is companion

area or kodomain from function f, is Kf = {4,5,6,7,8}

c. Range or output area from function f is Rf = {4,5,6}

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