Answer key
1 Functions: An introduction
1·1 1. DA = {−4, −2, 3, 5}
2. RA = {0, 1, 4, 9}
3. DB = {−9, −7, 2, 3, 5, 6}
4. RB = {−2, −1, 0, 1, 3}
5. DC = {−5, −2, 3, 4, 9}
6. RC = {−1, 0, 1, 2, 3}
7. A−1 = {(4, −2), (1, 5), (0, −4), (9, −4), (1, 3)}
8. B−1 = {(3, −7), (0, 2), (1, −9), (3, 3), (−2, 6), (−1, 5)}
9. C−1 = {(1, −2), (2, 3), (−1, 4), (3, −5), (0, 9)}
1·2 1. B and C
2. C−1
3. No. Many students have cell phones as well as land lines at home at which they can be reached.
4. No, calling a home land line may reach the student or any other member of the family.
5. Yes, a person may legally have only one Social Security number.
6. Yes, each Social Security number issued is unique to a given person.
7. Yes, a person only has one birthday.
8. Possibly not. Does anyone in your class have the same birthday?
1·3 1. 20
2. −7
3. −3n + 2
4. 11
5. 1/2
6. 
7. 5
8. 1
9. 
1·4 1. 6
2. 
3. −1
4. 4
5. 104
6. −4
7. x ≠ 4
8. x ≠ −1/5, 1
9. x ≥ −2
10. x ≤ 10
1·5 1. The graph of the parabola moves left 2 units, is stretched from the x-axis by a factor of 3 units, and slides down 1.
2. The graph of the absolute value slides to the right 1 unit and down 3 units.
3. The graph of the square root function slides to the left 1 unit and up 2 units.
4. The graph of the parabola is reflected over the x-axis, stretched from the x-axis by a factor of 2, and slides up 3 units.
5. The graph of the absolute value function slides to the left 2 units, is reflected over the x-axis, stretched from the x-axis by a factor of 1/3, and slides up 5 units.
1·6 1. 
2. 
3. 
4. 
1·7 1. b, d
2. a, d
2 Linear equations and inequalities
2·1 1. a = −3
2. y = 3.7
3. x = 6
4. 
5. 
6. q = 24.5r
7. Kristen has 445 classical and 3225 rock songs on her MP3 player.
8. Diane bought 25 plants at $6.50 each and 65 plants at $4.50 each.
2·2 1. 
2. 
3. 
4. 
5. 
6. 
2·3 1. (4, −3)
2. (−5, 1)
3. (4.5, 6.5)
4. (−2, −5)
5. (7, 0)
6. (−1, 8)
7. 
8. (12, −5) + ˙ ˙ ˙.
2·4 1. (3, −7)
2. (−5, 2)
3. (−10, 12)
4. (6.3, 5.2)
5. (−12.6, 13.8)
2·5 1. (7, −3)
2. (−8, 5)
3. (120, 135)
4. 
5. (8.4, 4.2)
6. 
2·6 1. (2, −3, 4)
2. (5, 2, −4)
3. (7, 0, −2)
4. 
2·7 1. (5, −8)
2. (−3, 11)
3. 
4. (40, 26, 85)
5. (3, 0, 2)
6. 
7. (2, 5, 9, 4)
8. (10, −5, 8, −4)
2·8 1. Advance sale $7.50, at the door $9, adult $15
2. 250 pre-performance student tickets; 300 student tickets on the day of the performance; 700 adult tickets
3. B is worth 17 point, A is worth 13 points, E is worth 11 points, and R is worth 19 points.
2·9 1. 
2. 
3. 
2·10 1. −5, 1
2. −1, 11
3. −5, 2
4. 1/5, 3
5. −1, 5
6. 3, 10
2·11 1. −1 ≤ x ≤ 9
2. x < −5 or x > −1
3. x ≤ −1 or x ≥ 2.5
4. 
5. |x + 2| < 4
6. |2x − 5| ≥ 7 (This is equivalent to |x − 2.5| ≥ 3.5 but uses integers in its expression.)
3 Quadratic relationships
3·1 1. x = −2
2. (−2, −17)
3. y ≥ −17
4. x = 4.5
5. (4.5, 17.5)
6. y ≤ 17.5
7. (5, 0) and (6,0)
8. 
9. (−3, −1)
10. x = −3
3·2 1. 4x2 (2x2 − 3x + 5)
2. (4x − 3)(8x2 + 3x − 9)
3. (10x + 7y)2
4. 25(2w − v)2
5. 9(3t + 4)(3t − 4)
6. (3x + 2y + 3)(3x − 2y + 5)
7. 2(2x + 3)(4x2 − 6x + 9)
8. (6 − 5k)(36 + 30k + 25k2)
3·3 1. (3x − 5)(4x + 11)
2. (8x + 9)(6x + 7)
3. (6x + 13)(4x − 5)
4. (12x + 7)(3x + 4)
5. (10x − 9)(5x − 6)
6. (6x + 5)(9x + 4)
7. (12x − 25)(4x + 9)
8. (8x − 15)(3x + 10)
3·4 1. f(x) = (x − 3)2 − 4
2. 
3. 
4. 
5. 
6. 
7. 
8. 
3·5 1. 
2. 
3. 
4. x = −2, 14
5. 
3·6 The function is s(t) = −16t2 + 64t + 40
1. 104 ft
2. 0.65 and 3.35 sec (answer to nearest hundredth)
3. 4.55 sec
The function is s(t) = −4.9t2 + 19.6t + 15
4. 34.6 m
5. 1.03 and 2.97 sec (answer to nearest hundredth)
6. 4.66 sec
7. 600 items
8. $360,000
9. $75,000
10. $285,000
11. P(x) = −x2 + 1100x − 15000
12. The company begins to make money when between 13.81 and 1086.19 units are sold. It loses money when less than 13.81 or more than 1086.19 units are sold.
13. 550
14. 287,500
3·7 1. Domain: x ≥ −3; inverse function: 
2. Domain: x ≥ 5; inverse function: 
3·8 1. (x + 5)2 + (y − 2)2 = 82
2. Center: (−4, 9); r = 9
3. Center: (6, 0); r = 
4. Center: (−7, 10); r = 13
5. Center: (21, −60); r = 71
3·9 1. 
2. 
3. 
4. 
3·10 1. Center: (4, −5); vertices: 
asymptotes: y + 5 = ± 2(x− 4)
2. Center: (−5, 4); vertices: 
asymptotes: 
3. 
4. 
3·11 1. 
2. (−7, −1), (1, 7)
3. 
4 Complex numbers
4·1 1. i
2. −1
3. i
4. i
5. −64
6. 
7. −45
8. 
4·2 1. 13 + 2i
2. 10 − 2i
3. 23 − 2i
4. 
5. 
6. 
7. 
8. x = 3, y = −2
4·3 1. Discriminant = 0; roots are real, rational, and equal
2. Discriminant = 204; roots are real, irrational, and unequal
3. Discriminant = −79; roots are complex numbers
4. Discriminant = 4; roots are real, rational, and unequal
5. 
6. 
4·4 1. Sum = 
product 
2. 3
3. 5
4. 36x2 −17x − 35 = 0
5. 81x2 − 270x + 127 = 0
6. 64x2 − 80x + 97 = 0
5 Polynomial functions
5·1 1. Even
2. Neither
3. Odd
4. Neither
5. Even
5·2 1. x ≤ 
2. Reals
3. 5
4. −7
5·3 1. x → −∞, f(x) → ∞; x → − ∞, g(x) → − ∞
2. x → −∞, g(x) → −∞; x → −∞, g(x) →−∞
3. x → −∞, k(x) → −∞; x → −∞, k(x) →−∞
4. x → −∞, p(x) → −∞; x → −∞, p(x) →−∞
5·4 1. Yes
2. Yes
3. (4x + 3) (5x − 4)(3x + 7)
4. (5x + 3)(3x − 4)(2x + 7) (8x − 15)
6 Rational and irrational functions
6·1 1. x ≠ 2, 3
2. 
3. y → 0
4. 
5. 
6. 
7. 
8. 
9. 
10. 
6·2 1. 
2. 
3. 
4. 
5. 
6. 
6·3 1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
6·4 1. 
2. −1, 27
3. 4, 12
4. 
5. 4, 
6. −4
7. 40, 60, 120 farads
6·5 1. 
2. y ≥ 5
3. 
4. y ≤ 7
5. x ≤ 3 or x ≥ 9
6. y ≥ 0
7. −8 ≤ x ≤ 4
8. 0 ≤ y ≤ 6
6·6 1. 
2. 
3. 
4. 6
5. 
6. 
7. 
6·7 1. 26
2. −15
3. 9
4. −9, −8
5. 12
6. 15
7 Exponential and logarithmic functions
7·1 1. 10x5y5z5
2. 250x7
3. 2000x7
4. 
5. 
6. 1
7. 2x3
8. 27
9. 
10. 
11. 
12. 10y + 15
7·2 1. log9(6561) = 4
2. 
3. 102 = 100
4. 
5. Domain: 
Range: real numbers
6. Translate right 4; stretch from the x-axis by a factor of 2; translate up 1
7·3 1. 
2. 
3. 
4. 
5. 
6. 
7. x + y + z
8. y −x
9. 
10. 
7·4 1. 
2. 
3. ± 13
4. 5
5. 1.83
6. 0.76
7. a. 0.003981
b. 0.00000001
8. Lemon juice is an acid and sea water is a base.
8 Sequences and series
8·1 1. 7 + 11 + 15 + 19 + 23
2. 2 + 9 + 28 + 65
3. 85 + 90 + 95 + 100
4. 4 + 10 + 28 + 82
5. 
6. 
7. 
8. 
8·2 1. 16, 25, 34, 43, 52
2. 72, 66, 60, 54, 48
3. 20, 100, 500, 2500, 12,500
4. 7, 22, 67, 202, 607
5. 17, 28, 45, 73, 118
6. 
7. 20
8·3 1. 641
2. 1588
3. 1196
4. 209
5. 719
6. 814
8·4 1. 15,480
2. 4220
3. 11,880
4. 102,375
5. 6480
6. 25,710
8·5 1. 4,718,592
2. 
3. 
4. 
5. 8,388,608
6. $14,482.98
8·6 1. 4,194,300
2. 3,486,784,400
3. 240,000
4. 
5. 98,301
9 Introduction to probability
9·1 1. 30
2. 10,368 (repetition of flavors is allowed)
3. 744
4. 362,916
5. 5040
6. n2 − n
7. (7!)(.25 min) = 1260 min = 21 hr (The guys probably didn’t take all the pictures.)
9·2 1. 15,120
2. 151,200
3. 5040
4. 1260
5. 42,840
6. 95,040
7. 
8. The order could be Will, Peter, and seven other batters; or Peter, Will, and seven other batters. There are two ways in which Will and Peter can be arranged and 13P7 ways the remaining players can be placed in the line-up. The probability is 
9·3 1. 210
2. 495
3. 22C7 =170,544
4. 
5. 
6. Five of the cards contain lengths that represent right triangles (3, 4, 5; 5, 12, 13; 1,
2; 11, 60, 61; 7, 24, 25). Selecting three cards from these five and one card from the remaining three has probability 
9·4 1. 32x5 + 80x4y + 80x3y2 + 40x2y3 + 10xy4 + y5
2. x6 − 12x5y + 60x4y2 − 160x3y3 + 240x2y4 − 192xy5 + 64y6
3. 7,838,208a5b4
4. −8064x5
5. 
6. −489,888x4
9·5 1. 
2. 
3. 
4. No. p(student is a member of the orchestra) × p(student is a member of the honor society) = 
= 
does not equal p(student is a member of the orchestra and honor society) = 
5. 
6. 
7. No. p(person is between 21 and 24) × p(person listens to music 2–3 hr per day) = 
= 
does not equal p(person is between 21 and 24 and listens to music 2–3 hr per day) = 
9·6 Decimal answers for this exercise should be rounded to four decimal places.
1. 
2. 
3. 
4. 
5. 
10 Introduction to statistics
10·1 1. Mean = 12.49 mm; median = 11.8 mm
2. Mean = 10.358 sec; median = 10.305 sec
3. Mean = 80.0086; median = 80
4. Mean = 997.516 hr; median = 1025 hr
10·2 1. IQR: 15 mi; sample standard deviation: 10.4 mi
2. a. Mean: 71,956.3; median: 69,885
b. IQR: 5967; sample standard deviation: 5758.4
3. a. Mean: 456.2 calories; median: 415 calories
b. IQR: 160 calories; population standard deviation: 157.2 calories
4. The calories from McDonald’s sandwiches have a lower measure of center than do the sandwiches offered by Burger King. There is less variation for the sandwiches offered by McDonald’s. Although McDonald’s has three sandwiches which constitute outliers in the spread of calorie ranges, these sandwiches have fewer calories than the highest calorie-rated sandwich from Burger King.
10·3 1. P(61 < h < 63.5) = 0.341
2. P(56 < h < 66) = 0.954
3. P(h > 63.5) =.5 − P(61 < h < 63.5) =.5 − 0.341 =.159
4. P(h < 66) =.5 − P(61 < h < 66) = 0.5 + 0.476 = 0.977
5. P(h < 56 or h > 66) = 1 − P(56 < h < 66) = 1 − 0.952 = 0.045 (see question 2)
6. P(h < 58.5 or h > 66) = 1 − P(58.5 < h < 66) = 1 − 0.819 = 0.181
7. P(11.7 < volume < 12.2) = 0.5205
8. P(volume < 12.1) = 0.7161
9. P(volume > 12.4) = 0.0766
10. P(volume < 11.65 < or volume > 12.35) = 0.4795
11. P(t > 4.5) = 0.0401
10·4 1. a. 
b. Yes, r = 0.9816
c. Price = 124,364 × (1.00085)x
d. The price of the house multiplies by a factor of 1.00085 for each additional square foot of area.
e. $657,104
2. a. 
b. Yes, r = 0.999097
c. Calories = 9.021 × fat − 1.322
d. The number of calories in the sandwich increases by 9.023 for each additional gram of fat in the sandwich.
e. 179.1 calories
3. a. 
b. Exponential
c. Price per share = 4.36884(1.52216)year – 2000; (r = 0.977394)
d. The price of the Apple stock in 2006 was approximately $54.34.
4. a. 
b. The correlation coefficient for the exponential model is −0.99929, while the correlation coefficient for the linear model is −0.995451. The data are best supported by an exponential model.
c. Number = 1010.01(0.595621)time
d. The number of radioactive nuclei after 0.5 sec is approximately 779.
5. a. 
b. Power function
c. Distance = 0.1116 × speed1.9997
d. The stopping distance on a wet road with tires having poor tread from a speed of 58 mph is 375.108 ft.
6. a. 
b. Power
c. yr = 0.999988 × dist1.50036 (Kepler’s third law of planetary motion)
d. The time needed for the planetoid Ceres to make a complete revolution of the sun is approximately 4.438 years.
7. a. 
b. Logarithmic
c. Wind chill = 13.349 − 7.5506 ln (wind speed)
d. The wind chill when the air temperature is 10°F and the wind is blowing at 35 mph is approximately −13.5°F.
11 Inferential statistics
11·1 1. The survey is biased because of geography. The opinions of those people who live in the northeastern part of the United States do not necessarily represent those of the entire country.
2. Access a database for all registered voters in the United States. (a) Randomly select a large number of voters from this set of data and ask them to respond to a survey. (b) Randomly select a large number of voters within each state and ask them to respond to a survey. (Do you have a different thought? Ask your teacher to evaluate your response.)
11·2 1. 0.933
2. 1.28
3. 0.041
4. 0.018
For questions 5–7, the mean = 67.2 and the standard error of the mean 
= 0.481.
5. P(66.5<
<67.9) = 0.855
6. P(<68.5)=0.5+P(67.2<<68.5) = 0.997
7. P(>66)=0.5+P(66<<67.2) = 0.994
For questions 8–10, the proportion = 0.98 and the standard error =
8. P(0.975 < p < 0.99) = 0.733
9. P(p > 0.995) = 0.5 – P(0.98 < p < 0.995) = 0.008
10. P(Less than 1% fail) = P(more than 99% meet manufacturer’s specs) = 0.5 − P(0.98 < p < 0.99) = 0.055
11·3 1. 1.75
2. −0.75
3. 1.6
4. A = 80.02, B = 94.38
5. A = 825.14, B = 982.86
6. invNorm(0.01, 1.002, 0.03) = 0.93 liters
7. invNorm(0.96, 16, 1.2) = 18.1 hands
11·4 1. $340.48 to $363.88
2. 11,258 to 12,141
3. 32.41% to 57.59%
11·5 1. H0: The mean is greater than or equal to 1.01
Ha: The mean is less than 1.01
Decision: Fail to reject the null hypothesis
Interpretation: There is no evidence to support the claim that the mean weight is different from the manufacturer’s claim.
2. H0: The proportion of dentists who recommend sugarless gum is 0.6
Ha: The proportion of dentists who recommend sugarless gum is less than 0.6
Decision: The proportion of dentists who recommend sugarless gum is 0.5625. Because this point is not inside the critical region, fail to reject the null hypothesis.
Interpretation: There is no evidence to suggest that less than 60% of the dentists recommend sugarless gum.
3. H0: The mean number of overtime hours each week is less than or equal to 40.4
Ha: The mean number of overtime hours each week is greater than 40.4
Decision: Reject the null hypothesis
Interpretation: The data supports management’s claim that the number of overtime hours worked each week is increasing.
4. H0: The proportion of rock-and-roll love songs played on the radio is greater than or equal to 0.5
Ha: The proportion of rock-and-roll love songs played on the radio is less than 0.5
Decision: Because 48 of the 125 songs, or 38.4%, were “love” songs, reject the null hypothesis.
Interpretation: The evidence supports Jack’s claim that less than 50% of the rock-and-roll songs played on the radio are “love” songs.
11·6 Describe a simulation that can be used to determine an answer to each of these problems.
1. Designate the numbers 0–4 to represent the different dinosaurs. Use a random number generator (such as randint(0,4,n) where n represents the number of boxes of cereal purchased) to determine the number of boxes of cereal that need to be purchased before the consumer gets one of each of the values 0 through 4. Repeat to get a large number of trials.
2. Designate the numbers 0–54 to indicate that the Western team wins a game and the numbers 55–99 to indicate that the Eastern team wins. Each trial can be randint(0,99,7). Read from left to right to determine which group reaches four wins first. Repeat to get a large number of trials.
12 Trigonometry: Right triangles and radian measure
12·1 1. 74.2
2. 72.5
3. 171.6
4. 17
5. 45
6. 41
7. 202
12·2 1. 2
2. 
3. 
4. 
5. 
6. 1
7. 
8. 2
9. 
10. 
11. 
12. 
13. 
14. 
15. 
16. 
17. 
18. 
19. 
12·3 1. 479, −241
2. 77, −283
3. 263, −457
4. 85
5. 10
6. 70
7. 23
8. tan 37
9. −sin41
10. −cos51
11. 
12. 
13. 
14. 
15. 
12·4 1. 
2. 
3. 
4. 40°
5. 50°
6. 75°
7. 2.5
8. 
12·5 1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
12·6 1. 219 in2
2. 3019 ft2
3. 75° or 105°
4. 141°
12·7 1. 28.6°
2. 36.0°
3. XZ = 40.2 cm, YZ = 50.6 cm
4. QS = 8.1 cm, RS = 7.2 cm
5. ES = 47.1 cm, EY = 55.3 cm
6. QE = 42.7 cm, ED = 56.5 cm
12·8 1. 1
2. 1
3. 1 (82 > 44)
4. 1 (length of the side opposite the obtuse angle is greater than the length of the adjacent side)
5. 0 (length of the side opposite the obtuse angle is less than the length of the adjacent side)
6. 2 (length of the opposite side is greater than the minimum length 72 sin(50) ≈ 55.16, but less than 72)
7. 2 (length of the opposite side is greater than the minimum length 125 sin(57) ≈ 104.83, but less than 125)
12·9 1. 39 cm
2. 115 ft
3. 44.5°
4. 112.8°
5. 54.6 N
6. 93°
7. 36.0°
13 Graphs of trigonometric functions
13·1 1. 8
2. 4
3. f(19) = f(3) = 4
4. f(−203) = f(5) = −4
5. 8. The graph is stretched from the x-axis by a factor of 2 and then translated down 1 unit. The range of f(x) is −4 ≤ y ≤ 4, while the range of g(x) will be −9 ≤ y ≤ 7. The amplitude is 
13·2 1. The graph of the sine function is translated down 1 unit.
2. The graph of the cosine function is translated up 1 unit.
3. The graph of the sine function is translated right 
unit.
4. The graph of the cosine function is translated left 
unit.
5. The graph of the tangent function is translated right 
unit.
6. The graph of the tangent function is translated down 1 unit.
7. The graph of the sine function is stretched from the x-axis by a factor of 2.
8. The graph of the sine function is stretched from the y-axis by a factor of 
.
9. The graph of the cosine function is stretched from the y-axis by a factor of 
.
10. The graph of the cosine function is stretched from the y-axis by a factor of 
, stretched from the x-axis by a factor of 2, and translated down 1 unit.
11. The graph of the sine function is translated right 
, reflected over the x-axis, and stretched from the x-axis by a factor of 
.
12. The graph of the tangent function is stretched from the y-axis by a factor of 
.
13. The graph of the sine function is translated left 
stretched from the x-axis by a factor of 2, and translated up 1.
14. The graph of the cosine function is shifted left 
, stretched from the x-axis by a factor of 2, reflected over the x-axis, and translated up 3 units.
15. Amplitude: 2; period: 2 π; phase shift: left 
vertical translation: up 1
16. Amplitude: 2; period: 2 π; phase shift: right 
vertical translation: up 3. (An acceptable answer would be a phase shift left by 5π/6, or right by 7π/6. Since multiplying cos by −1 induces a phase shift right by π, on top of a phase shift right by π/6, you get a phase shift right by 7π/6, or a phase shift left by 5π/6.)
17. Because the period of the sine function is 2π, sin(z) = sin(z + 2π) = h.
18. Because the period of the cosine function is 2π, cos(z) = cos(z + 2π). However, cos(z + 3π) will be another half revolution about the cycle, so cos(z + 3π) = −k.
19. 
20. 25.4 ft
21. 
13·3 1. 
2. 
3. 
4. 
5. 
13·4 1. 228.6°, 311.4°
2. 60.9°, 240.9°
3. 0°, 60°, 300°
4. 19.5°, 160.5°
5. 16.6°, 124.8°, 196.57°, 304.8°
6. 0°, 60°, 180°, 300°
7. 38.7°, 321.3°
8. 23.0°, 157.0°, 219.8°, 320.2°
9. 0°, 120°, 240°
10. 0°, 45°, 135°, 180°, 225°, 315°
11. 2.6 and 9.9 hr after high tide