Sac 1 Revision Questions 1

7/28/2019 Sac 1 Revision Questions 1

1/12

Multiple-choice questions

1 For the function with rulef(x) = , which of the following is the maximal domain?

A (, 25]

B [5, 5]

C (, 25]

D (25, )

E [25, )

2 Iffis a function for which the rule isf(x) = x, wherex is real, the rule for the inverse

functionf1 is:

A f1(x) = +x

B f1(x) =

C f1(x) =

D f1(x) = x

E f1(x) = x

3 Forf: [ 1, 5)R,f(x) =x2, the range is:

A R

B [0, )

C [0, 25)

D [4, 25]

E [0, 5]

Evans, Lipson, Jones, Avery 2006 1

Essential Mathematical Methods 3 & 4 CAS Teacher CD-ROMChapter 1 Functions and relations: Test A


2/12

4 A function has rule,f(x) = 5x1/3 1,x R. The rule for the inverse function is:

A f1(x) = 1

B f1(x) =

C f1(x) = ()3

D f1(x) = 35

1+x

E f1(x) = 5x3 + 1

5 (2, 6) (, 3] =

A (, 2)

B (, 6)

C (2, 3]

D (6, 3)

E (2, 6)

6 (2, 6) (3, 3] =

A (3, 6)B (, 6]

C (2,)

D (3, 2)

E (2, 3]

7 Which of the following functions is not one-to-one?

A f(x) = 9 x2,x 0

B f(x) = 9

C f(x) = 1 9x

D f(x) =

E f(x) =




3/12

8 The functionf: (3, 4] R,f(x) =x2 3 has range:

A (6, 13)

B [ 3, 13]

C (0, 6)

D [0, 13]

E (3, 6]

9 The range of the function with graph as shown is:

A R

B (1, 12)

C (0, 3)

D [4, 12)

E [0, 12)

10 State the maximal domain of the function with rulef(x) =

A R\{5}

B R\{0}

C R+

D [5, )

E (5, )


x

y

4

(4, 12)

(2, 0) 4



4/12

11 The range of the function with rulef(x) = |x 4| + 3 is:

A (4, )

B R

C [3, )

D (4, )

E (1, )

12 Forf: (a, b] R,f(x) = 5 x where a < b the range is:

A (5 a, 5b)

B (5 a, 5 b]

C (5 b, 5 a)

D (5 b, 5 a]

E [5 b, 5 a)

13 Iff(x) =x2 + 1 andg(x) = 2x + 1 thenf(g(a)) =

A 4a2 + 4a + 1

B 4a

C 4a2

+ 4a + 2D 4a2 + 1

E 2a2 + 1

14 Iff(x) = then the range offis:

A (, 10]

B (, 2)

C (, 2]

D [2, ) (2, 0]

E R

15 For the function with rulef(x) = ,f(a + 2) +f(a 2) =

A

B

C

DE




5/12




6/12

Short-answer questions (technology-free)

1 Sketch the graph off: [1, 5] R,f(x) = 2x + 3 and state the range of this function.

2 For the functionf: [1, 4] R,f(x) = 2x2

a state the range off

b state the rule and domain of the inverse functionf1

c on the one set of axes sketch the graphs offandf1

3 Find the inverse,f1, of the functionf:R\{ } R,f(x) = . State the domain and range of

the inverse function.

4 Sketch the graph off: [3, ) R, f(x) = and find the inverse functionf1. Sketch the

graph off1 on the same set of axes.

5 Sketch the graph off:R\{0} R, f(x) = + 3 and on the same axes sketch the graph of

f1. State the domain and range off1.

6 Letf: [2, ) R,f(x) = 3 + 4x. Findf1, stating the rule, domain and range, and sketch

the graph ofy =f(x) andy =f1(x) on the one set of axes.

7 Iff(x) = |x | andg(x) =x2 2x + 3 find:

a f(g(1))

b g(f(1))

c f(g(2))

d g(f(2))

8 Forf(x) = |x | 5 andg(x) =x2 5 findf(g(x)) andg(f(x)) and state the range of the

functions with ruley =f(g(x)) andy =g(f(x))




7/12

Extended-response questions

A piece of fencing 240 m long will be used to enclose

three sides of a rectangular field.

The fourth side has a brick wall.

Let l(m) be the length of the field as shown. LetA

(m2) be the area of the field.

brick wall

l (m)

1 ExpressA as a function ofl.

2 What is a suitable domain of the function?

3 Use a graph to determine the range ofA.




8/12

Answers to Chapter 1 Test A

Answers to multiple-choice questions

1 A

2 D

3 C

4 C

5 C

6 A

7 B

8 B

9 D

10 E

11 C

12 E

13 C

14 A

15 E

Answers to short-answer (technology-free) questions

1




9/12

range = [7, 5]


0

(1, 5)

(5, 7)

3



10/12

2 a [2, 32]

b f1(x) = and domain = [2, 32]

c

3 domain=R\{},f1(x) = , range =R\{}

4 f1(x) =x2 + 3


0

(1, 2)

(2, 1)

(4, 32)

(32, 4)

y =f(x)

y =f1(x)

0

3

3

y =f1(x)

y =f(x)



11/12

5 f1(x) = , domain =R \{3}and range =R\{0}


y

0

3

3

y =f(x)



12/12

6

f1(x) =

domain = [5, ), range = [2,)

7 a 2

b 2

c 11

d 3

8 f(g(x)) = |x2 5| 5, range = [5, );g(f(x)) =x2 10 |x | + 20, range = [5, )

Answers to extended-response questions

1, 2 A(l) = l(240 2l) where 0 < l< 120

3 (0, 7200]


(5, 2)

3

y =f(x)

y =f1(x)


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Sac 1 Revision Questions 1