1. 1. ARE YOU READY TO STUDY TODAY ??COME ON WE SAY : CHEER UP
2. 2. FUNCTIONS, EQUATIONSAND QUADRATICINEQUALITIESDIAH PERMATASARI
3. 3. RELATION and function
4. 4. 1. Explanation Relation & FunctionSequence couple & Cartesiusproduct Relation function
5. 5. DefinitionNumber Pair (x, y) with x is first order and y is second order thensaid 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 productcompilation A and B is all compilation sequence couple (x,y) with x Aand y B. write : A x B = {(x,y) | x A and y B}For Example 2.2 :A = {4,5,6} and B= {0,2}, definite :a. A x Bb. 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)}
6. 6. DefinitionFor example A x B is Cartesius product compilation A and B, thenrelation R from A to B is compilation of any kind part for Cartesiusproduct 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 componentcompilation 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 62
7. 7. Compilation-compilation R1, R2, and R3 is part compilation forcartesius product A x B is a familiar as relation for compilation Ato compiltion B.From on explanation, the relation R = {(x ,y) | x A and y 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 B that is output area (range) relation R.
8. 8. DefinitionRelation from compilation A to compilation B that isfunction or cartography, if each element(component) on compilation A exact form a pair onlywith a element (component ) on compilation B.For example f is a function or cartography fromcompilation A to compilation B, then function f can besymbol with f :AB
9. 9. 0 0Picture 2.3. The 0 function f can be write 0that is f : x y = f (x) 0For example, x A, y B that (x,y) f , then y is chart or imagination from xby function f. the chart or imagination can be said with y = f(x), you can see apicture 2.3. So, the function f can be write that is f : x y = f (x)for example, f : A B, thena. Origin area (domain) function f is compilation A and the symbol with Dfb. Companion area (kondomain) function f is compilation B and thesymbol with Kf , andc. Output area (Range) function f is compilation from all chart A in B andthe symbol with Rf.
10. 10. Example1. What is a diagram a function or not, and give reason ? F H A ABB aak k b bl l ccm m d d
11. 11. Answer :a. Relation F is function because every component compilation A connection with exact one component compilation B.b. Relation H isnt function because be found one component compilation A, that c isnt use companion in B2. Definite domain, kodomain, and range from function f the indication by bow and arrow diagram ? FA B Answer : a. Compilation A = {a,b,c,d} is origin area or a.>domain from f is Df = {a,b,c,d} .4b..5 b. Compilation B = {4,5,6,7,8} is companion>.6area 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}