modul 1 fungsi.doc

KERTAS 1

MODUL 1 / TG4: FUNGSI

KERTAS 1

1.Rajah 1 menunjukkan hubungan antara set A dan set B.

Diagram 1 shows the relation between set A and set B.

Rajah 1

Diagram 1

Nyatakan

State(a) julat hubungan itu,

the range of the relation,

[1 m / Aras R](b) jenis hubungan itu.type of the relation.

[1 m / Aras R]



Rajah 2

Diagram 2

Nyatakan

State(a) objek bagi 2,

the object of 2,

[1 m / Aras R]

(b) julat hubungan itu,

the range of the relation,

[1 m / Aras R]

(c) kodomain hubungan itu.

the codomain of the relation.

[1 m / Aras R]

3.

R = {a, b, c}

S = {b, d, f, h, j}

Berdasarkan maklumat di atas, hubungan antara R dan S ditakrifkan sebagai hubungan bertertib {(a, b), (a, d), (b, f), (b, h)}.Based on the above information, the relation between R and S is defined by the set of ordered pairs {(a, b), (a, d), (b, f), (b, h)}.

Nyatakan

State(a) imej bagi a,

the images of a,

[1 m / Aras R](b) objek bagi b.the object of b.

[1 m / Aras R]

4.Hubungan antara dua pembolehubah diberi sebagai {(3, 3), (2, 0), (1, 3), (0, 6)}.

The relation between two variables is given by {(3, 3), (2, 0), (1, 3), (0, 6)}.

Nyatakan

State (a) objek bagi (3,the object of 3,

[1 m / Aras R]

(b) domain bagi hubungan ini,the domain of this relation, [1 m / Aras R]

(c) jenis hubungan.the type of relation.

[1 m / Aras R]



Rajah 5

Diagram 5

(a)Wakilkan hubungan di atas dalam bentuk set hubungan bertertib.

Represent the above relation in set of ordered pairs.

[1 m / Aras R]

(b)Nyatakan imej bagi 1.

State the images of 1.

[1 m / Aras R](c)Nyatakan jenis hubungan.

State the type of the relation.

[1 m / Aras R]

6.Rajah 6 menunjukkan fungsi f dan fungsi g. Fungsi f memetakan x kepada y dan

fungsi g memetakan y kepada z.

Diagram 6 shows the function f and the function g. Function f maps x to y and

function g maps y to z.

SHAPE \* MERGEFORMAT

Rajah 6

Diagram 6

Determine

(a)

[1 m / Aras R]

(b)

[1 m / Aras R]

7.Rajah 7 menunjukkan fungsi linear g.

Diagram 7 shows the linear function


Rajah 7

Diagram 7

(a) Nyatakan nilai bagi k.

State the value of k.

[1 m / Aras R](b) Dengan menggunakan tatatanda fungsi, ungkapkan g dalam sebutan x.

Using the function notation, express g in terms of x.

[1 m / Aras R]

8.Rajah 8 menunjukkan graf bagi fungsi h(x) bagi domain 0 x 5.

Diagram 8 shows the graph of function h(x) for domain 0 x 5.

Rajah 8

Diagram 8

Tentukan

Determine

(a) objek bagi 3,

the objects of 3,

[1 m / Aras R]

(b) julat bagi fungsi itu.

the range of the function.

9.Rajah 9 menunjukkan fungsi g di mana .

Diagram 9 below shows function g where .


Rajah 9

Diagram 9

Cari nilai bagi m dan n.

Find the value of m and n.

[3 m / Aras S]

10.Diberi fungsi , cari

Given the functions , find

(a)

, [1 m / Aras S]

(b)nilai-nilai x yang mungkin supaya .

the possible values of x such that .

[2 m / Aras T]

11.Rajah 11 menunjukkan fungsi , dengan keadaan k ialah pemalar.

Diagram 11 shows the function , where k is a constant. SHAPE \* MERGEFORMAT

Rajah 11

Diagram 11

Cari nilai bagi k.

Find the value of k.

[2 m / Aras S]

12.Diberi fungsi dan , cari

Given the function and, find

(a)

, [1 m / Aras S]

(b)nilai bagi k dengan keadaan .

the value of k such that . [2 m / Aras S]

13.Diberi bahawa dan , dengan keadaan k dan

m adalah pelamar. Cari nilai-nilai bagi k dan m.

Given that and , where k and m are

constants. Find the values of k and m.

[3 m / Aras S]

14.Diberi bahawa dan .

Given the function and .

Cari

Find

(a)

, [2 m / Aras S]

(b)

. [2 m / Aras S]

15.Fungsi f ditakrifkan sebagai . Diberi bahawa .

Function f is defined as . Given that .

Cari

Find

(a)nilai k,

the value of k,

[2 m / Aras S]

(b)seterusnya, fungsi .

thus, the function .

[2 m / Aras S]

16.Fungsi h ditakrifkan sebagai .

The function h is defined as .

Cari

Find

(a)

, [2 m / Aras S]

(b)

. [1 m / Aras S]

17.Diberi bahawa , find

Given that , find

(a)

, [2 m / Aras S]

(b)nilai bagi .

the value of .[1 m / Aras S]

18.Diberi fungsi songsang bagi ialah , cari nilai-nilai m

dan n.

Given that the inverse function of is , find the values of

m and n. [3 m / Aras S]

19.Rajah 19 menunjukkan graf bagi fungsi , untuk domain .

Diagram 19 shows the graph of the function, for the domain .

Rajah 19

Diagram 19

Nyatakan

Sate

(a) nilai bagi v,

the value of v,

[2 m / Aras S]

(b) julat bagi f(x) sepadan dengan domain yang diberi.

the range of f(x) corresponding to the given domain.

[2 m / Aras S]

20.Maklumat berikut merujuk kepada fungsi f dan g.

The following information refers to the function f and g.

Cari .

Find .

[3 m / Aras S]


Given the function and , find

(a)

, [2 m / Aras S]

(b)

. [2 m / Aras S]

22.Diberi fungsi dan . Cari.

Given the function and . Find

(a)

, [2 m / Aras S]

(b)

. [2 m / Aras S]

23.Diberi fungsi , cari

Given the function , find

(a)

, [1 m / Aras S]

(b)nilai p dengan keadaan .

the value of p such that .[2 m / Aras S]


Given the function and , find

(a)f(x), [1 m / Aras S]

(b)nilai k dengan keadaan .

the value of k such that . [2 m / Aras S]

25.Diberi fungsi , dengan keadaan a dan b adalah pemalar dan b > 0 dan

fungsi gubahan . Cari nilai-nilai bagi a dan b.

Given the function , where a and b are constant and b > 0 and the

composite function . Find the values of a and b.

[3 m / Aras T]

26.Diberi fungsi dan fungsi gubahan , cari

Given the function and the composite function , find

(a)

, dalam sebutan k,

, in terms of k,

[2 m / Aras T]

(b)nilai x apabila .

the value of x when .

[2 m / Aras T]


Given the function dan , find

(a)

, [2 m / Aras S]

(b)

. [2 m / Aras T]

28. Diberi fungsi f(x) = x+1. Cari fungsi g jika fg(x) = x2 + 3x + 5

[4 m/Aras T]

KERTAS 2

1. Rajah 1 mewakili pemetaan y kepada x oleh fungsi dan pemetaan y

kepada z oleh fungsi , .

Diagram 1 shows the mapping of y to x given by the function and the

mapping of y to z given by the function , .

Rajah 1

Diagram 1

Carikan

Find

(a) nilai a dan nilai b,

the values of a and b,

[2 m / Aras S]

(b) fungsi yang memetakan x kepada y,the function that maps x to y,

[2 m / Aras T]

(c) fungsi yang memetakan x kepada z.the function that maps x to z.

[2 m / Aras T]

2. Diberi dan .

Given and .

Carikan

Find

(a) , [2 m/ Aras S](b) nilai k supaya .

the value of k such that .

[3 m / Aras T]3.Diberi . Carikan

Given . Find

(a)

dalam sebutan k dan m,

in terms of k dan m,

[2 m/ Aras S]

(b)nilai k dan nilai m, jika dan .

the values of k and m, if and .

[4 m/ Aras T]

4.Rajah 4 menunjukkan skala bagi suhu dalam Celsius ((C) dan Fahrenheit ((F) pada suatu termometer. Hubungan antara suhu dalam x (C dan y (F diberi oleh , dengan keadaan k ialah pemalar.Diagram 4 shows the scales of temperature in degree Celsius ((C) anddegree Fahrenheit ((F) on a thermometer. The relationship between temperature in x (C and y (F is given by function, where k is a constant.

Rajah 4

Diagram 4

(a) Cari nilai k.

Find the value of k.

[2 m / Aras S]

(b) Jika suhu hari ini ialah 32(C, apakah suhu dalam (F?

If today's temperature is 32(C, what is the temperature in (F?

[2 m / Aras S]

(c) Bentukkan satu fungsi yang membolehkan kita menukar suhu dari unit darjah Fahrenheit ((F) kepada darjah Celsius ((C).

[2 m/ Aras T] Set B

Set A

p

q

r

8

6

4

2

0

1

2

3

4

2

4

6

8

Set B

Set A

3

f

x

y

z

10

2

g

0

2

4

6

(2

0

k

4

x

g(x)

x

y

y = h(x)

0

1

3

2

(2

x

g(x)

x

EMBED Equation.3

EMBED Equation.3

3

4

f(x)

x

0

(F

(C

212

100

50

122

32

0

(4

(20

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modul 1 fungsi.doc

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