College Algebra - MAC1105Practice Test 4 -- (Sections 4.1 - 4.6)

The skills and level of understanding needed to solve the following problems are necessary to do well on theupcoming exam. It is recommended that students attempt these problems as if they were taking an exam, andcheck the answers with the key on the last page. Please seek assistance from myself during office hours or thetutors in BB207 as needed.

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Determine whether or not the function is one-to-one.1)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

A) No B) Yes

1)

2) f(x) = 4x3 - 8A) Yes B) No

2)

3) f(x) = 16 - x2A) No B) Yes

3)

If the function is one-to-one, find its inverse. If not, write "not one-to-one."4) {(19, 5), (10, -1), (-19, 7)}

A) {(19, -1), (19, 10), (7, -19)} B) {(5, 19), (-1, 10), (7, -19)}C) not one-to-one D) {(5, 19), (-19, 10), (7, -1)}

4)

5) {(12, 1), (-10, 1), (11, -14)}A) {(12, 1), (1, -10), (-14, 11)} B) not one-to-oneC) {(1, 12), (11, -10), (-14, 1)} D) {(1, 12), (1, -10), (-14, 11)}

5)

6) f(x) = 2x + 3

A) f-1(x) = x + 32

B) not a one-to-one

C) f-1(x) = x2 - 3 D) f-1(x) = x - 3

2

6)

1

Nott7 nd

Xodd

2

Xeven Not l Z lx 4 CyX

T2 1O

y 2 32YI33 2y2 2 Of x

7) f(x) = (x - 6)2

A) f-1(x) = x + 6 B) f-1(x) = 1x + 6

C) not a one-to-one D) f-1(x) = x + 6

7)

8) f(x) = x3 - 8

A) f-1(x) = 3x + 8 B) not a one-to-one

C) f-1(x) = 3x + 8 D) f-1(x) =

3x - 8

8)

For the function as defined that is one-to-one, graph f and f-1 on the same axes.9) f(x) = x + 4

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

A)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

B)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

D)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

9)

2

f ftt

µo

C4,0 Los 4i l Us 3

3071in.IE Yo's cosg sFty r 3 5,3 3,5

XO

x

10) f(x) = x3 + 2

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

A)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

B)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

D)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

10)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Use the alphabet coding method (A =1, B = 2, C = 3, ... Z = 26) to solve the problem.11) The function defined by f(x) = x + 2 was used to encode a message as:

15 3 22 10 9 7 16 11 23 21Find the inverse function and determine the message.

11)

3

i

X72

I

0AT

ugmn IIy Xt2X yt2

MA T It

y X 2 7 5 14 9 21 18

G e N i v s

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the function value. If the result is irrational, round your answer to the nearest thousandth.12) Let f(x) = 4x. Find f(3).

A) 256 B) 81 C) 64 D) 1212)

13) Let f(x) = 16x. Find f(-2).

A) - 136

B) 36 C) 136

D) -12

13)

14) Let f(x) = 4x. Find f 52.

A) 512 B) 10 C) 1.741 D) 32

14)

Graph the function.15) f(x) = 4x

A)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

B)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

C)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

D)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

15)

4

T La2 62 36

0A 4512 25 32

xI

0

X

16) f(x) = 12x

A)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

B)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

C)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

D)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

16)

Find the future value.17) $5789 invested for 9 years at 5% compounded quarterly

A) $9028.86 B) $8980.64 C) $9053.67 D) $9070.4817)

Find the present value of the future value.18) $2000, invested for 9 years at 5% compounded monthly

A) $3088.69 B) $3133.69 C) $1321.45 D) $1276.4518)

Solve the problem.19) If $4000 is invested in an account that pays interest compounded continuously, how long will it

take to grow to $8000 at 7%?A) 12.1 years B) 9.9 years C) 10.0 years D) 4.9 years

19)

20) Find the required annual interest rate, to the nearest tenth of a percent, for $5100 to grow to $6300 ifinterest is compounded quarterly for 5 years.

A) 1.1% B) 4.2% C) 2.1% D) 5.3%

20)

5

I 1 21 21

xp EFIlo r OI 05 E LX

x xA 4

P A n 42

Far i O

n 4A

A P Itf or A continuously

Graph the exponential function using transformations where appropriate.21) f(x) = 2x+2 - 1

A)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

B)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

D)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

21)

Solve the equation.

22) 2(5 + 3x) = 116

A) {4} B) 18

C) {3} D) {-3}

22)

23) 16 = b2/5A) {1024} B) {-4, 4} C) {4} D) {-1024, 1024}

23)

24) a3/5 = 8A) {32} B) {-32, 32} C) {-2, 2} D) {2}

24)

25) 64x - 1 = 163x

A) - 1 B) - 6 C) - 16

D) - 12

25)

Evaluate the logarithm.

26) log8164

A) -2 B) 2 C) -8 D) 8

26)

6

2531 24g z 45 5

Qu 351730

27) log10 0.0001

A) -0.0004 B) -4 C) 4 D) 0.0001

27)

Write in logarithmic form.28) 163/4 = 8

A)log4 8

log3 16 = 16 B) log16 8 = 3

4C) log8 16 = 3

4D) log3 16 = 3

4

28)

Write an equivalent expression in exponential form.

29) log25 5 = 1

2

A) 251/2 = 5 B) 51/2 = 25 C) 525 = 2 D) 12 5 = 25

29)

Solve the equation.

30) log7 149

= x

A) 17

B) {-2} C) 1343

D) {2}

30)

31) x = 9log9 2

A) {9} B) {18} C) {2} D) {-2}31)

32) log1/3(x + 5) = -3A) 27 B) 22 C) 42 D) 32

32)

7

X 2

n

O3 11 5

33 111 527 111 5x

Graph the function. Give the domain and range.33) f(x) = log2 x

A) domain: (-∞, 0); range: (-∞, ∞)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

B) domain: (0, ∞); range: (-∞, ∞)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

C) domain: (0, ∞); range: (-∞, ∞)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

D) domain: (-∞, 0); range: (-∞, ∞)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

33)

8

X G o

f i 210924 2 8,3

10928 3

x

34) f(x) = log1/5 (x + 4)

A) domain: (-4, ∞); range: (-∞, ∞)

x-8 -6 -4 -2 2 4 6 8

y8

6

4

2

-2

-4

-6

-8

x-8 -6 -4 -2 2 4 6 8

y8

6

4

2

-2

-4

-6

-8

B) domain: (-∞, ∞); range: (4, ∞)

x-8 -6 -4 -2 2 4 6 8

y8

6

4

2

-2

-4

-6

-8

x-8 -6 -4 -2 2 4 6 8

y8

6

4

2

-2

-4

-6

-8

C) domain: (0, ∞); range: (-∞, ∞)

x-8 -6 -4 -2 2 4 6 8

y8

6

4

2

-2

-4

-6

-8

x-8 -6 -4 -2 2 4 6 8

y8

6

4

2

-2

-4

-6

-8

D) domain: (-∞, ∞); range: (0, ∞)

x-8 -6 -4 -2 2 4 6 8

y8

6

4

2

-2

-4

-6

-8

x-8 -6 -4 -2 2 4 6 8

y8

6

4

2

-2

-4

-6

-8

34)

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/orreflected.

35)

x-10 -8 -6 -4 -2 2 4 6 8

y10

8

6

4

2

-2

-4

-6

-8

-10

x-10 -8 -6 -4 -2 2 4 6 8

y10

8

6

4

2

-2

-4

-6

-8

-10

A) log2(x - 1) - 1 B) log2(x - 1) + 1 C) log2(x + 1) + 1 D) log2(x + 1) - 1

35)

9

logax 02 I

am 10924 4220 4

10924 D l logditDH logditD Ilogdo I 10922 1 logic I

ITI l 1error or

Match the function with its graph.36) f(x) = log5 (x - 1)

A)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

B)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

C)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

D)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

36)

Solve the problem. Round your answer to the nearest tenth, when appropriate. Use the formula pH = -log H3O+ , asneeded.

37) Find the pH if [H3O+] = 6.7 × 10-5 .A) - 5.8 B) 4.6 C) 4.2 D) 5.8

37)

38) Find [H3O+] if the pH = 1 .4.

A) 4.0 × 10-1 B) 2.5 × 10-1 C) 4.0 × 10-2 D) 2.5 × 10-238)

Solve the problem.39) The loudness of a sound can be quantified in units called decibels, where the number of decibels d

is given by the formula d = 10 log II0.

What is the decibel rating of a sound having an intensity I = 1000 I0?A) 3 decibels B) 1000 decibels C) 13 decibels D) 30 decibels

39)

Use the change of base rule to find the logarithm to four decimal places.40) log7 3

A) -0.5646 B) 1.7712 C) 1.1292 D) 0.564640)

10

faith shifts leftf X h shifts right

logft I logsti

Iii

pit log 6.7 105 4.20O

O

109,3 17 0.5646

Match the function with its graph.41) f(x) = log3 (-x)

A)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

B)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

C)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

D)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

41)

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables representpositive real numbers.

42) loga(4x6y)

A) (loga4 )(logax) (logay) B) loga4 + (logax)6 + logay

C) loga(4 + x6 + y) D) loga4 + 6logax + logay

42)

43) log8 4 78

A) log8 4 + 12log8 7 - log8 8 B) (log8 4)

12log8 7 - log8 8

C)log8 4 +

12log8 7

log8 8D) log8 4 + log8 7 - log8 8

43)

11

44) log2 x9 y77

A) ( log2 x)9 + (log2 y)

7 - log2 7 B) (9 log2 x)(7 log2 y) ÷ log2 7

C) 9 log2 x + 7 log2 y + log2 7 D) 9 log2 x + 7 log2 y - log2 7

44)

45) logb3 x6

y2z8

A) 6logbx - 2logby - 8logbz B) 2logbx - 23logby -

83logbz

C) 13logbx6 - logby2 - logbz8 D) 2logbx ÷ (

23logby ∙

83logbz)

45)

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers witha ≠ 1 and b ≠ 1.

46) log6 13 - log6 x

A) log6 (13 - x) B) log12 13x

C) log6 x13

D) log6 13x

46)

47) log3 m + log3 n

A) log3 mn

B) log3 m ∙ log3 n C) log3 (m + n) D) log3 mn

47)

48) 3 loga x - 9 loga z2

A) loga 3x9z2

B) loga x3

z11C)

loga x3

loga z18D) loga

x3

z18

48)

Solve the equation. Round to the nearest thousandth.49) 2x = 23

A) {4.524} B) {2.442} C) {0.221} D) {11.500}49)

50) 3(3x - 3) = 24A) {1.964} B) {3.667} C) {1.693} D) {-0.036}

50)

51) 7 3x = 8 (x + 1)A) {-15.573 } B) {0.553} C) { 1.069 } D) {2.069 }

51)

Solve the equation. Give the answer in exact form.52) e2x - 8ex + 15 = 0

A) {e5, e3} B) 5e, 3e

C) {ln (-5), ln (-3)} D) {ln 5, ln 3}

52)

12

log yl log Gthlogy'tlogzy log

91092 710924 10927

A 3 3 3 ln24ln In TnsO 34311343 3 zy.gezt3z lzne2n4ztl 1.964

2 8 1502Nodecimals

E 3 Le 57 0C

ex 3 0 ex 5 0332 51

503 eX 5

X ln X ln5

Solve the equation and express the solution in exact form.53) log 2 x = log 5 + log (x - 2 )

A) 3 B) { 103} C) { 2

3} D) - 10

7

53)

54) log9 (x - 5) + log9 (x - 5) = 1

A) { 26} B) {8} C) {-8, 8} D) {- 26, 26}

54)

Solve the problem.55) At what interest rate must $5000 be compounded annually to equal $7116.56 after 9 yr? (Round to

the nearest percent.)A) 6% B) 5% C) 4% D) 3%

55)

56) The population growth of an animal species is described by F(t) = 400 log(2t + 3) where t ismeasured in months. Find the population of this species in an area 6 months after the species isintroduced.

A) 74 B) 470 C) 704 D) 240

56)

57) Use the formula P = Iekt. A bacterial culture has an initial population of 10,000. If its populationdeclines to 6000 in 6 hours, what will it be at the end of 8 hours?

A) 2531 B) 5061 C) 2000 D) 6000

57)

58) Find the doubling time for an amount invested at a growth rate 6% per year compoundedcontinuously.

A) 7.4 years B) 11.6 years C) 4.2 years D) 10 years

58)

59) How long will it take a sample of radioactive substance to decay to half of its original amount, if itdecays according to the function A(t) = 250e-.223t, where t is the time in years? Round your answerto the nearest hundredth year.

A) 24.76 yr B) 55.75 yr C) 27.87 yr D) 3.11 yr

59)

60) A certain radioactive isotope has a half-life of approximately 1500 years. How many years to thenearest year would be required for a given amount of this isotope to decay to 70% of that amount?

A) 450 yr B) 702 yr C) 772 yr D) 2605 yr

60)

13

nloga I

0 591 6577FIFE's resected

Answer KeyTestname: PILOTPRACTICETEST4

1) AID: CA12L 4.1.1-1

2) AID: CA12L 4.1.1-10

3) AID: CA12L 4.1.1-11

4) BID: CA12L 4.1.3-4

5) BID: CA12L 4.1.3-5

6) DID: CA12L 4.1.3-10

7) CID: CA12L 4.1.3-17

8) AID: CA12L 4.1.3-12

9) CID: CA12L 4.1.4-4

10) DID: CA12L 4.1.4-5

11) f-1(x) = x - 2; MATH GENIUSID: CA12L 4.1.6-5

12) CID: CA12L 4.2.1-1

13) BID: CA12L 4.2.1-4

14) DID: CA12L 4.2.1-9

15) CID: CA12L 4.2.2-1+

16) BID: CA12L 4.2.2-2+

17) CID: CA12L 4.2.6-1

18) DID: CA12L 4.2.6-6

19) BID: CWA11B 3.3.2-1

20) BID: CA12L 4.2.6-9

21) DID: CA12L 4.2.3-10+

22) DID: CA12L 4.2.5-7

23) DID: CA12L 4.2.5-8

24) AID: CA12L 4.2.5-9

25) AID: CA12L 4.2.5-12

26) AID: CA12L 4.3.1-2

27) BID: CA12L 4.3.1-9

28) BID: CA12L 4.3.1-16

29) AID: CA12L 4.3.1-22

30) BID: CA12L 4.3.2-2

31) CID: CA12L 4.3.2-5

32) BID: CA12L 4.3.2-15

33) CID: CA12L 4.3.3-1+

34) AID: CA12L 4.3.3-6+

35) DID: CA12L 4.3.4-1

36) AID: CA12L 4.3.3-12

37) CID: CA12L 4.4.3-1

38) CID: CA12L 4.4.3-5

39) DID: CA12L 4.4.3-10

40) DID: CA12L 4.4.6-1

41) BID: CA12L 4.3.3-15

42) DID: CA12L 4.3.5-1

43) AID: CA12L 4.3.5-3

44) DID: CA12L 4.3.5-7

45) BID: CA12L 4.3.5-10

46) DID: CA12L 4.3.5-11

47) DID: CA12L 4.3.5-12

48) DID: CA12L 4.3.5-16

49) AID: CA12L 4.5.1-1

50) AID: CA12L 4.5.1-3

51) BID: CA12L 4.5.1-7

52) DID: CA12L 4.5.1-11

53) BID: CA12L 4.5.2-5

54) BID: CA12L 4.5.2-4

55) CID: CA12L 4.5.4-5

56) BID: CA12L 4.6.1-5

57) BID: CA12L 4.6.1-12

58) BID: CWA11B 3.3.3-4

59) DID: CA12L 4.6.2-2

60) CID: CA12L 4.6.2-6

14