,16758&725
$16:(56
&2//(*(0$7+(0$7,&6)25
%86,1(66(&2120,&6/,)(6&,(1&(6
$1’62&,$/6&,(1&(6
)2857((17+(‘,7,21
5D\PRQG%DUQHWW
Merritt College
Diagnostic Prerequisite Test
Section references are provided in parentheses following each answer
to guide students to the specific content in the book where they can
find help or remediation.
1. (A) (y+z)x (B) (2 +x)+y (C) 2x+3x (A.1)
2. x
3
–3x
2
+4x+8 (A.2) 3. x
3
+3x
2
–2x+12 (A.2)
5
2
13. (A) 4.065 *10
12
(B) 7.3 *10–
3
(A.5) 14. (A) 255,000,000
(B) 0,000 406 (A.5) 15. (A) T (B) F (A.1) 16. 0 and –3 are two exam-
5
5
4
2
2
ANSWERS
Chapter 1
x
x
10. –6…x…-1 11.
x
…4 12. xÚ9 13. 1–8, 24 14.
3
–1, 5
2
y
20.
m
=14 21. y6-
15
22. x7-
10
y
=
2
x
30.
y
=–
6
31. m63
6
32. u61
6
3
13. Slope =
1
4; y int. =
2
3 14. Slope =
1
5; y
int. =– 1
2
19. Slope =
7; x int. =–7 20. Slope =– 9
2; x
int. =
9 21. y=2x+1
6
25. x int.: 1
2; y int.:
1; y=–2x+1 26. x int.: 1; y int.: 3; y=–3x+3
29. y
30. y
31.
y
ANSWERS
1
Answers A-3
86. (A) p=0.0005x–1.7 (B) p=–0.0005x+7.8 (C) (9,500, 3.05)
x
2.80
9,800
Demand
9,2000
Dollars
47. x=4,
y=–3 48. x=–5;
y=6 49. x=–1.5,
y=–3.5
7 x–1 57. y=–3.2x+30.8
59. (A) m=
2
y
=
2
61. (A) m=–5
y
63. (A) Not defined (B) x=5 (C) None 65. (A) m=0 (B)
y
=5
(C)
y
=5 66. (A) Not defined (B)
x
=2 (C) None 67. The graphs
72. (A) C=39x+1,905 (B) C
(C) The y int., $1,905,
is the fixed cost,
210
(3.5, 205.56)
225
Barometric Pressure
(inH
g
)
79. (A) T=70 –3.
6
A (B) 10,000 ft 80. (A) T=3.2A+200
x
9.5
9
4,2000004,3
Dollars
Demand
Exercises 1.3
(C) 67.2 kg (D) 5′9.5″ 3. (A) P=0.445d+14.7 (B) The rate of
change of pressure with respect to depth is 0.445lb/in.2 per ft. (C) 37 lb/in.2
9. (A) y
100
(B) The rate of change of fossil fuel
production is –0.19
%
per year.
0.5
10.50
Licensed Drivers
(millions)
Population (milli
o
(B) 2025 (B) 2029
x
40200
Licensed Drivers
Population (millions)
15. (A) S
600
300
(B) $662 billion
Chapter 2
1. y
x
x
2. y
3. y
4. y
x
x
x
2
21. Linear 22. Neither 23. Neither 24. Linear 25. Linear
26. Neither 27. Constant 28. Constant
29. y
x
x
5
30. y
5
31. y
10
32. y
x
5
33. y
x
5
34. y
x
5
35. y
x
10
36. y
37. y
5
38. y
5
5
x
39. y=0 40. y=0 41. y=4 42.
y
=3
43. x=–5 44. x=5 45. x=–
6
46. x=–5,
49. All real numbers except –4 50. All real numbers
55. No; for example, when x=0, y={2 56. Yes; all real numbers except 0
57. Yes; all real numbers except 0 58. No; when x=0, y={3 59. No;
y
2
2
76. (A) –3x–3h+9 (B) –3h (C) –3 77. (A) 4x2+8xh +4h2–7x–7h+6
86. (A) p
$2,000
2
(B) xR(x)
5 8,500
(C) R(x)
$15,000
89. (A) P
1
x
2
=59x–3x
2
–125,
1…x…20
8 155
20 –14
5
15
90. (A) P
1
x
2
=1,500x–60x
2
–4,000,
1…x…25
(B) xP(x)
5 2,000
20 2,000
25 –
4,000
(C) P(x)
x
25
$5,000
ANSWERS
85. (A) p(x)
$100
Exercises 2.2
A-8 Answers
y int.: 12 (B) Vertex:
1
4, –4
2
(C) Min.: –4 (D) Range: yÚ-4
or
3
–4, ∞
2
28. Vertex form:
1
x–3
22
–4 (A) x int.: 1, 5;
1
2
3
2
1
1
4
1
2
1
4
1
3
1
2
3
34. (A) –1.
5
3, 6.
5
3 (B) 0.36, 4.64 (C) No solution 35. 651.0417
9.08; y int.: –7 (B) Vertex:
1
3, –9.25
2
(C) Min.: –9.25 (D) Range:
y
3
2
–0.58, 8.58; y int.: –1 (B) Vertex:
1
4, –4.2
2
(C) min.: –4
.
2 (D) Range:
y
Ú-4.2 or
3
–4.2, ∞
2
39. f1x2=–0.121x–422+3.12 (A) x int.:
.
1
y
1
4
–8.
5
7, 2.
5
7; y int.: 3.30 (B) Vertex:
1
–3, 4.65
2
(C) max.: 4.65
(D) Range: y…4.65 or
1
–∞, 4.65
4
41. 1–∞,
–52h13,
∞2
1
2
1
3
70. (A) R
x
16,000
25
(B) 16.667 (16,667 computers);
$16,667,000 (C) $1,000
66. (A)
x 5101520253035
A-10 Answers
Copyright © Pearson Education, Inc.
50. (A) x int.: {1; y int.: –3
4
(B) Vertical asymptote: x=–2, x=2;
51. (A) x int.: 6; y int.: –4 (B) Vertical asymptotes: x=–3,
x
=2; horizontal
asymptote: y=0 (C) f(x)
10
(D) 10
f1
2
2
210 10
1
2
f1
2
55.
f1
x
2
=4x–x
3
56.
f1
x
2
=x
3
–x
57. (A) C
1
x
2
=180x+200
180x+200
x
600
30
59. (A) C1n2=
2,500 +175n+25n
2
n
(B)
1,500
C(n)
60. (A) C1x2=
2
x
(B)
500
61. (A) C1x2=
0.000481x–5002
3
+60,000
x
63. (A) (B) 1.7 lb
66. (A) 55 words per minute
60
67. (A)
68. (A) (B) 2.5
A-12 Answers
73. Decreasing:
1
0, 1
4
3
1
f1
2
1
3
2
74. Decreasing:
1
–∞, 0
2
1
2
1
1
1
3
2
1
y
2
y
g
f1
2
y
y
1
1
y
y
g
18. (A)
5
y (B)
5
y (C)
5
y
(D)
y (2.2) 19.
f1
x
2
=–
1
x–2
22
+4. The graph of
1
72. (A) x intercepts: –.4, 8.4; y inter-
cept: 1.2 (B) Vertex: (4.0,
78.
y
=ce –
5
t (2.6) 79. If
l
o
g
1 x=y, then 1y=
x
; that is, 1 =
x
for
all positive real numbers x, which is not possible. (2.6) 80. The graph of
y
=2
3x is vertically expanded by a factor of 2, reflected in the x axis, and
shifted 1 unit left and 1 unit down. Equation: y=–22
81. G
1
x
2
=0.3
1
x+2
22
–8.1 (A) x intercepts: –7.2, 3.2; y intercept:
1
3
Copyright © Pearson Education, Inc.
–8.1 (D) Range:
83. (A) S1x2=µ3 if 0 …x…20
0.057x+1.86 if 20 6x…200
C
50
85. $5,269.51 (2.5)
x
40
R
x=27.314 thousand units (27,314
units); R6
C
for 1 …x64.
6
8
6
4.
6
8
6
6x627.314. (C) Maxi-
($500,000). This occurs at an output
of 20 thousand units (20,000 units).
1
2
sand units (4,686 units) and for
6
6
or 27.314 6x…40; p70 for
4.
6
8
6
6x627.314. (C) Maximum
profit is 160 thousand dollars ($160,000).
This occurs at an output of 16 thousand
units (16,000 units). At this output, the
wholesale price is p
1
16
2
=$30. (2.3)
x
300
near 190. (E) 86 ft; 194 ft (F) Maximum
2
91. (A) 2,833 sets
(B) 4,836 (C) Equilibrium price: $131.59; equi-
93. (A) N=2
2
t or N=4t (B) 15 days (2.5) 94. k=0.009 42; 489 ft
(2.6) 95. (A) 6,134,000 (2.6)
96. 23.1 yr (2.5) 97. (A) $1,319 billion
(B) 2031 (2.5)
Chapter 3
Exercises 3.1
i
6. S
l
o
p
e=300; y
int. =15,000 7. Slo
p
e=
5
0; y
i
nt. =2,000
8. Slo
p
e=17
5
; y
int. =5,000 9. 0.062 10. 8.5% 11. 13.7%
12. 0.0435 13. 0.0025 14. 0.19% 15. 0.84% 16. 0.0036 17.
1
25. $42 26. $85.50 27. $1,800 28. $250 29. 0.12 or 12% 30. 0.16
Exercises 3.2
(B) $27,527.90 41. $12,175.69 42. $174,250.55 43. All three graphs
are increasing, curve upward, and have the same y intercept; the greater the
45. Period Interest Amount
3 $117.44 $1,321.95
46. Period Interest Amount
0 $2,000.00
1 $165.00 $2,165.00
3 $193.35 $2,536.96
4 $209.30 $2,746.26
47. (A) $7,440.94
(B) $5,536.76
48. (A) $4,730.96
49. (A) $19,084.49
(B) $11,121.45
50. (A) $2,970.16
(B) 5.27% 54. (A) 3.09% (B) 2.99% 55.
112
80. 8,021 days; 18.310 yr
81. Years Exact Rate Rule of 72
82. 83. 14 quarters 84. 17 months
85. To maximize earnings, choose 10%
simple interest for investments lasting
86. To maximize earnings, choose 9% simple interest for investments lasting
fewer than 154 months and 6% compounded monthly otherwise. 87. 3.33%
Exercises 3.3
15. FV =$13,435.19 16. FV =$4,164.59 17. PMT =$310.62
ANSWERS
Answers A-15
25. n=
ln a1+i
FV
PMT b
26. i=
FV
–2 27. Value: $84,895.40;
43.
Payment
Unpaid
Balance
Unpaid
Copyright © Pearson Education, Inc.
less than 9 years and 9% compound interest for investments lasting 9 years or
more. (3.2) 20. $164,402 (3.2) 21. 7.83% (3.2) 22. 9% compounded
24. 288% (3.1) 25. $1,725.56 (3.1) 26. $29,354 (3.2) 27. $18,021 (3.2)
28. 15% (3.1) 29. The monthly payments with 0% financing are $450. If
34. 10.45% (3.2) 35. (A) 174% (B) 65.71% (3.1) 36. $725.89 (3.3)
37. (A) $140,945.57 (B) $789.65 (C) $136,828 (3.3, 3.4) 38. $102.99;
3 265.82 12.81 253.01 259.33
4265.81 6.48 259.33 0.00
50. 6.33% (3.1) 51. 44 deposits (3.3) 52. (A) $1,189.52 (B) $72,963.07
(C) $7,237.31 (3.4) 53. The certificate would be worth $53,394.30 when the
(3.2, 3.3, 3.4) 54. The lower rate would save $12,247.20 in interest
payments. (3.4) 55. $3,807.59 (3.2) 56. 5.79% (3.2) 57. $4,844.96 (3.1)
Chapter 4
Exercises 4.1
1
1
1
6. (22.5, 3) 7. y–7=–6
1
x–2
2
8. y–20 =21x–32
1
1
1
2
1
2
1
56.
1
1.232, –3.347
2
57. y
8
( 4, 1)
(2, 4)
x2y6
58. y
10
x y 3
(3, 4)
59. y
10
1
1
1
1
ANSWERS
67. (A) p=1.5x+1.95 (B) p=–1.5x+7.8 (C) Equilibrium price:
$4.875; equilibrium quantity: 1.95 billion bushels (D)
p
6
Equilibrium
point
Supply
curve
(B)
Profit
y
x
$300,000
200
Break-even
point
line
Cost
line
(B) 1,920
Cost
line
(1,920, 38,304)
Break-even point
Loss
x
3,000
Cost
