LKS Relasi Dan Fungsi

LKS Relasi dan Fungsi (SMA kelas X)

LEMBAR KERJA SISWA SISWA ( LKS ) A. B. C. ". '.

Judul LKS :Relasi dan Fungsi Mata Pelajaran : Matematika Kelas  Semester : X! Al#kasi $aktu : %& menit K#metensi "asardan!ndikat#r "asar dan!ndikat#r Penaaian *. menunjukkankemamuanmenjela menunjukkankemamuanmenjelaskankem+alik#n skankem+alik#nserelasi. serelasi. %. menunjukkankemamuanmenjela menunjukkankemamuanmenjelaskankem+alik#n skankem+alik#nsedaera,asa sedaera,asal-l- daera,kaandaera,kaandandaera,,asilsuaturelasi. /. menunjukkankemamuanmenjela menunjukkankemamuanmenjelaskankem+alisi0at1si0atrelas skankem+alisi0at1si0atrelasii

F. Petunjuk Belajar : Se+elummengerjakanmasala,+eriku Se+elummengerjakanmasala,+erikutse+aikn2akam tse+aikn2akamumem+aa+uk umem+aa+ukusisa.Carita,utentangr  usisa.Carita,utentangr  elasi dan 0ungsi. 3. 4ugas 5. Petunjuk : *. Kerjakantugas 2ang adaadalem+arke adaadalem+arkegiatanseara+e giatanseara+erkel#m#k rkel#m#k 2ang 2ang tela,di+entuk. tela,di+entuk. %. "iskusidengantemankel#m#km "iskusidengantemankel#m#kmuu /. Akan ditunjuksearaaakakildarikel#m ditunjuksearaaakakildarikel#m#kuntukmela# #kuntukmela#rkan,asildiskusin2 rkan,asildiskusin2aa Kerjakan Soal berikut

*. Per,atikan,imunan Per,atikan,imunan A dan B +erikutini +erikutini A 6 7Ruia,- Ruee- Ba,t- Ringgit8 B 6 7!nd#nesia- !ndia- 4,ailand- Mala2sia8 "aatka,Andameli,atadan2a, "aatka,Andameli,atadan2a,u+unganantara u+unganantara,imunanAdan ,imunanAdan B9 Jelaskan : ............................................ ................................................................... .............................................. .............................................. .............................................. ......................... ............................................ ................................................................... .............................................. .............................................. .............................................. ......................... ............................................ ................................................................... .............................................. .............................................. .............................................. ......................... %. Per,atikanemat,imunan+erikutini Per,atikanemat,imunan+erikutini C67Jakarta- L#nd#n- Cair#- Beijing8 - "67!nd#nesia- !nggris- Mesir- C,ina8 '67!nd#nesia- Brail- ;igeria- Siss8-F67Asia-Amerika-A0rika-'r#a8 Siss8-F67Asia-Amerika-A0rika-'r#a8 4entukanasangan,imunan 2ang daatmemun2ai,u+unganda daatmemun2ai,u+ungandanjelaskan,u+un njelaskan,u+ungann2a gann2a Jaa+: ............................................ ................................................................... .............................................. .............................................. .............................................. ......................... ............................................ ................................................................... .............................................. .............................................. .............................................. ......................... ............................................ ................................................................... .............................................. .............................................. .............................................. ......................... ............................................ ................................................................... .............................................. .............................................. .............................................. .........................

LKS Relasi dan Fungsi (SMA kelas X) /. !sila, diagram . ?langikem+aliseerti n# / dengan,imunan1,imunanadas#al n# % Jaa+: A B

@. 4entukantitiktitikadak#rdinatkartesius+erikutse,inggamemerli,atkan,u+unganada  jaa+ans#al n# /  

Mala2sia   4,ailand  

!ndia

  !nd#nesia Ruia,Ruee Bat, Ringgit . Buatla,5imunanasangan+erurutandariK##rdinatkartesius adajaa+ans#al n# @ Jaa+ : ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... . Ria- Budi- dan'd2gemar+ermain+ulutangkis. 'k#danAndigemar+ermain +#la +asket. Ali gemar+ermain+ulutangkisdan +#la +asket. a. Jika A adala,,imunannamaanakdan B adala,,imunanermainan- maka : 4unjukkanla,relasi di atasdengan diagram ana,D

LKS Relasi dan Fungsi (SMA kelas X)  +. ;2atakanla,relasiterse+utdengan,imunanasangan+erurutan A B Jaa+:

A E B 6 7(Ria- ..................................... )- (Budi- .....................................)- (................. Bulu tangkis)- (............ - .....................)- (............. - ..........................)(............. - ..........................)8 . 4uliskan hubungan  darisetia diagram ana,+erikutini

G. Buatla,kesimulan+agaimanadaatterjadin2a,u+unganantara % ,imunanD ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... *&. Per,atikan diagram ana,

LKS Relasi dan Fungsi (SMA kelas X)

a. 4entukan,u+ungandarisetia diagram ana,+erikutD  +. "iagram ana,mana 2ang semuaangg#tan2amendaatasanganangg#ta,imunan B9 ......................................................................................................................................... **. "iagram ana, 2ang setiaangg#ta,imunan A mendaat pasangantepatsatu adaangg#ta,imunan B dinamakan fungsiataudengansim+#l f  .Manaka, diagram ana,adas#al n# G 2ang meruakan0ungsi - +erikanalasann2a Jaa+ : ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... *%. "alam0ungsi,imunan A dinamakan "#main - ,imunan B dinamakank#d#main ,imunanangg#ta,imunan B 2ang mendaatasangandinamakan range 4entukan "#main- K#d#maindan range darisetia0ungsiadas#al n# *& Jaa+: ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... .......................................................................................................................................... ........................................................................................................................................ ......................................................................................................................................... .........................................................................................................................................  f  ( x)

*/. Se+ua,0ungsialja+ardaatdin2atakandengan  f  ( x)

=

=

 x

 y

=

 x

atau

 x

a. !sila,ta+el+erikutuntuk0ungsi  x G    f(x) /  +. Beraanilai E 2ang +eraki+atnilai yatau 0(E) tidakdaatditentukan

LKS Relasi dan Fungsi (SMA kelas X) Jaa+ : ......................................................................................................................................... ......................................................................................................................................... "alam0ungsialja+ar,imunansetianilai E 2ang 2angmeng,asilkannilai 2 2ang meruakan+ilanganriilmeruakandaera,asalatau "#main dari0ungsidan,imunannilai 2 2ang meruakan+ilanganriildinamakandaera,,asilatau Range dari0ungsi. *>. Per,atikan diagram +erikut.

(a) (+) () "iagram manaka, 2ang mende0inisikan0ungsi9 Jelaskan. ............................................................................................................................................. ............................................................................................................................................. ............................................................................................................................................. ............................................................................................................................................. ............................................................................................................................................. ............................................................................................................................................. ............................................................................................................................................. ............................................................................................................................................. ............................................................................................................................................. *@. Suatu0ungsi f dari,imunan A ke,imunan B din2atakandenganaturan x2 - > x H /dengan x ∈ A. Jikadiketa,ui A 6 7*- %- /- >8 danB 6 71%- 1*- &- *- %- /- >8tentukan: a. 5imunanasangan+erurutandalam f   +. "aera, asal (domain)- daera,kaan ( kodomain)- dandaera,,asil ( range) dari f  Jaa+: E * % / > 0(E ) "0 6 ........................................ K0 6 ........................................ R0 6 ........................................ *. 4entukand#main dan range daris#al n# *% Jaa+ : ......................................................................................................................................... ......................................................................................................................................... *. "iketa,ui 0ungsi 0 6 √ 2 1 tentukan d#main dan range 0ungsi terse+ut agar 0ungsi memun2ai nilai (eta). Jaa+:  x −

LKS Relasi dan Fungsi (SMA kelas X) Agar 0(E) +ernilai real maka %E I *  & %E  ........ E  ........ Jadi- " 6 7E  .........................8 R 6 7E  ........................8 *. "iketa,ui 0ungsi 0 6

3  x + 6 2  x −5

tentukan d#main dan range 0ungsi terse+ut agar

0ungsi memun2ai nilai (eta).

Jaa+: Agar 0(E) +ernilai real maka en2e+ut dari ea,an terse+ut  & .................  & E  ........... Jadi- " 6 7E  .........................8 R 6 7E  ........................8 % x − *

*G. "i+erikan 0ungsi  f memetakan x ke y dengan rumus  y 6 rumus 0ungsi g 2ang memetakan  y ke x. Jaa+:

 x + /

% x − *

 y 6

 x + /

2 (E H /) 6 ............... E2 H ..... 6 ................ E2 1 ...... 6 1/2 I * E (...... 1 ......) 6 ................. …………………

E6

…………………

- 2  ..........

 f  ( x ) = / x − %

%&. "iketa,ui0ungsi  - ,itungla, : a. 0(%) +. 0(1%) . 0(EH*) d. 0(%EH@) Jaa+ : a. 0(%) 6 / (....) I % 6 .... 1 .... 6 .....  +. 0(1%) 6 / (....) I % 6 .... 1 .... 6 ..... . 0(E H *) 6 / (...........) I % 6 ................ 1 .... 6 ..... d. 0(%E H @) 6 / (..............) I % 6 ................ 1 .... 6 ..... %*. "iketa,ui f (% x I /) 6 > x I . 5itungla, nilai dari  f (). Jaa+: %E I / 6 .... %E 6 .... H / 6 .... E 6 .... 0() 6 > (.....) I  6 ....................

- x≠ 1 /. 4uliskan