Exercise Set 1.1
1. y = 2x + 4 2. y = -3x 3. y = -2 4. y = ½x + 1/4 5.
6. 3/4, (4,0), (0,-3) 7. -½, (9/2,0), (0,9/4)
8. 5/4, (-12/5, 0), (0,3) 9. -13/47, (-112/13, 0), (0,-112/47) 10. 0, (0,-19/4) 11. y = -3x +11 12. y = ½x + 1
13.
14. y = 14x + 143/10 15. y = 4.1x -12.3 16. x = -1 17. y = -6 18. y = 2x + 4 19. x = 12
20. y = 8
21.
22.
23.
24.
25.
26.
27.
28.
1
29.
30.
y = -19/4
31.
32.
33.
34.
35.
36.
x = -1
2
37.
39.
38.
40.
y
x = 12
(12, 0)
x
41. (a) 2/5, (3,0), (0,-6/5) (b)
(0, 37/5)
(0, -6/5)
42. (a) -3/7, (-14,0), (0,-6) (b)
3
43. (a) y = -6/5 (b) x = 3 44. (a) y = -6 (b) x =-14 45. y = 1, y = -7 46. x = 8, x = -4 47. no slope 48. 7/5
49. -8/5 50. 0 51. no slope 52. ½ 53. -7 54. 24 55. -2 56. 0 57. no slope 58. 4/7 59. x = 1
60. 7x - 5y = 59 61. 8x + 5y = 0. 62. y = 4 63. x = 12 64. y = ½x + 3 65. 14x + 2y = 3 66. y = 24x -9
67. y = -2x 68. y = -5 69. x = ½ 70.
73. (a) 3x + 7y = -18(b) 7x - 3y = 16
77. (a)
(b)
71. y = 3x - 8 72. (a) 2x -5y = 16 (b) 5x + 2y = -18
74. (a) 3 .(b)
75. 5y + 2x = 20, 5y -2x = 20. 76. y = -5x ± 20
78.(b) no (c) examine the slopes 79. t = -0.05x + 4000 80. 130 81. 166
82.
83.
(c)
(b)
(a)
(a)
(b)
(c)
(d) They are horizontal translations of each other.(d) They are vertical translations of each other. Each
Each graph may be obtained from (a) by moving it 3
graph may be obtained from (a) by moving it 4 units
units to the left or right.
Up or down.
84.
(f) They are each obtained from (a) by moving it 4 units up or
down and simultaneously moving it 3 units to the left or
right.
(d)
(e)
85. The second line is obtained from the first by moving it h units
horizontally and k units vertically.
(a)
(b)
87. (a) 2x + y = 6 (b) 2x - y = 4 (c) 4x + 3y = 2
(c)
88. (25/14, 46/7) 89.
Exercise Set 1.2
1 (a) C(x) = 2500 + 30x, R(x) = 45x, $166.67 (b) 15x - 2500 (c) $266.67 2. It reduces to $80 3. $500
4. $27 5. $33 6. C(x) = 0.4x + 2000, R(x) = 1.2x, P(x) =0.8x-2000, x =2500 7. C(x) = 0.8x +1000, overhead
=$1000, Marginal cost = $0.80 8. $30 and $3800. 9.C(x) =0.75x + 4500, R(x) =2.25x (b) $3.90 per item 10. p = 0.006x +22.8 11.A(t) = -950t +10,000. 5.26 yrs. 12. House = $90,000, Land = $10,000
13.
f(-2) = 11/2, f(0) = -3/2, f(2) = 2, f(5) = 8
14.
f(-1) = -3, f(1.5) =1, f(4) = 3 (Either end points may have equality in 14 and 15.)
4
15.
f(-2) = 1, f(1.5) = -1.5, f(5) = 7
16. -2, 3, 0
17. 2,2,3,6,6
18. 1,-1,1,3,1
19. (a) one intersection at (2,1) (b) two intersections at (0, 2) and (10, 6) 20. Three; (1/5, 3/5), (7/3, 5/3), (11/3, 7/3)
21.
22.
23.
24.
C(x)
T(19.999) = $116.99, T(20.001) = $123.51
rather earn $19,999
x
5
Exercise Set 1.3
1. (a)
(b)
(c) 4267.7
2. (a)
(b)
(c)
(d) Widening
y = 1108x + 10442
y = 688x + 6092
3. (a)
(b) 1.608
(c) It is widening
6
(f) $9,810
4.(a)
(b) R = 0.985237
5.(a)
(b)
(c) It was unattractive in the 1980s.
(c) 0.976633
(d) 7.2
6
From the data, there is certainly some correlation between number of wins
and bating average.
7
7. (a)
(b)
The money spent on each
form of advertising grows
changes the same way.
(c) It is unclear, the different forms of advertising could be reaching different consumers.
8. (a)
(b) 1077.3
9. For 1977 to 1982,
(c) 1997
For 1983 to 1986
10.(a) It changes after 1980 (x = 21) (b)
(c) Riding became safer (perhaps because of helmet usage, or some other reason.
11. (a)
(b)
(c) The divorce rate in the 1980s decreased.
12. (a)
(b) Something in the country resulted in the decrease, perhaps better health care.
8
(There is a lot of information on the web regarding this topic.)
13.
14. (a)
14. (b)
(c)
(d)
15.
16.
Exercise Set 1.4
1. Is a function 2. Is a function 3. Is a function 4. Is a function 5. Is not a function 6. Is a function 7. Is not a function 8. Is a function
9. D = {-1,1,2,12}, R = {3.5.9.23} 10. D ={2,3,5,7}, R = {-5,4,9,11} 11. D = {3,4,7,11},
R = {-5,11,19} 12. D = {-3,2,5,19} R = {3,5,7} 13. D = {3,7,9} R = {-5,2,5,11} 14. D = {2,3,5,6} R = {-1} 15. D = {4,5,9} R = {22,2,3,7} 16. D = {1,2,3,4} R = {5} 17. (a) -5 (b) -8 (c) 1 (d) 6x - 5 (e) 3x + 3h -5 18. (a) -1 (b) 7 (c) 1 (d) 18x2 -1(e) 2x2 +4xh +2h2
-1 19. (a) -1/3 (b) 0 (c) 4/3 (d) (2x + 1)/(4x - 3) (e) (x + h + 1)/(2x + 2h - 3) 20. (a) 0 (b) 0 (c) 12 (d) 48 (e)
9
21. 3 22. 5
23. m 24. 2x + 2h -5 25. 2x + h + 3 26. 4x + 2h + 3 27. 10x + 5h -4 28. 3x2 + 3xh + h2 29.
32.
33. (a) -4 < x < 4 (b)
(c) -4 < y < 4
34.(a) -4 < x < 4
(b)
(c) -4 < y < 4
35. (a) -4 < x < 4 (b)
36.(a) -4 < x < 4 (b)
(c) y $ 5
(c) y # 4
37. (a) x $ 0 (b)
38. (a) x $ -1/2 (b)
(c) y $ 0
(c) y $ 0
39. (a) x $ 4/3 (b)
(c) y $ 0
40. (a) -4 < x < 4 (b)
(c) y $ 0
10
30.
31.
41. (a) -4 < x < 4 (b)
42. x =/ 3/2 43. x =/ -5/2 44. x =/ -4/3, 3/2 45. x =/ -3,0,3 46. Not
47. Is 48. Is 49. Is 50. Is 51. Is 52. Is 53. Is 54. Is
(c) y $ 0
55.(a)
(b) $6.25
56. (a)
57.
(d)
58. (a) 7x + 5 (b) -x - 9 (c) 12x2 + 13x - 14
(b) 43 in (c) 58 in
59. (a) x2 + 2x - 3 (b)-x2 + 2x - 3 (c) 2x3 - 3x2 (d)
(b) -2x2 + 3x + 10 (c) 6x3 + 14x2 - 9x - 21 (d)
(c) ½(x3 +x2+ 5x + 5) (d)
62. (a)
(b) x
(b)
-4 < x < 4 68 (a) |x|
60. (a) 2x2 + 3x + 4
61. (a) x2+ ½x + 11/2 (b)x2- ½x +9/2
(b)
63. (a) 2x2 + 9 -4 < x < 4 (b) 4x2 + 12x + 12 -4 < x < 4
65. (a)
(b) $245 (c) $403
(c)
(d)
64. (a) x + 2 x $ 1 (b) x2 + 2 -4 < x < 4
-4 < x < 4 (b) x
66. (a) x
-4 < x < 4 (b) x x $ -1 69 (a) |x|
70. {x | x is in the domain of f and f(x) is in the domain of g}
72.
73.
74.
75.
-4 < x < 4 67. (a) x
-4 < x < 4 (b) x x $ -3/2
71. f(d) = g(b)
11
-4 < x < 4
76.(a) 5 (b) -5 (c) 5 (d) -6 77. (a) 5 (b) -5 (c) 6 (d) -5
78.
79.
80. For non integer values, Ceil(x) = flr(x) + 1
81.
82.
83. f(x) = x18, g(x) = 3x2 - 2x + 23
84. f(x) = x54,
g(x) =2x8 - 11x5 -2x + 19
85. f(x) =
g(x) =x2 - 3
86.
88. x .4 miles. 89. x .16 miles
87.
1. (a) 3, (b) -15 (c) 2x -2y2 + h (d) -4xy-2xk -9y2-9yk-3k2 (e) 4+h -2y2 (f) -4x-2xk-9-9k-3k2
(g) 2x -2y2, 4 -2y2 (h)-4xy -9y2, -4x-9
92. (a) 864 (b) 1600 (c)24x2y2 +24xy2 +8y2h2 (d)16x3y2 +8x3k (e) 96y2+48hy2 + 8y2h2 (f)48x3 +8x3k
(g) 24x2y2, 96y2 (h) 16x3y, 48x3 93. (a) 218 (b) -8 (c) 2x + h -2y2 (d)-4xy-2kx -9y2z2 -9kyz2-3z2k2
(e) -6y3z –3y3l +2z + l
Exercise Set 1.5
1.
(b) -1 (c) -1
2.
(b) 2 (c) 2
3.
(b) 3 (c) 3
4.
(b) -3 (c) -3
12
5.
(b) 1 (c) 1
6.
7.
(b) 1 (c) 1
8.
9.
(b)None (c) None
11.
(b) -5.9, -2.1
(b) -1 (c) -1
(b) -2, 0 (c) -2, 0
10.
(b) 1.4, 4.6 (c)
12.
(b) -1, 5
(c)
13.
(b) -5.2, 1.2
(14)
(c)
13
(b) None (c) None
(c) -1,5
15.
(b) -3,4, 1.4
16.
(b) -5, 1
(c) -5, 1
18.
(b) -3.7, 1.2
(c)
17.
(b) -1.2, 3.2
(c)
19.
(b) -1.3, 4.8
(c)
20.
(b) None
22.
(b) None
(c) None
(c)
21.
(b) -2.5, 1.2
(c)
14
(c) None
23.
(b) None
(c) None
24.
(b) None (c) None
25. (a) 144 ft (b) 6 sec 26. (a) 276 ft, 2.5 sec (b) 6.65 sec 27. x = 360 ft, y = 900 ft 28. x = 375 ft, y = 500 ft
29. x = 777.501 ft, y = 363.332 ft 30.(a) 250 (b) $350,000 (c) $1400 31.(a) 100 (b) 31,000 32. (b) 71 (c) $1185
33. (a) b2 -4ac < 0 (b) b2 -4ac < 0 and a > 0 (c) b2 -4ac < 0 and a < 0 34. y = 2x2 -3x + 10 35. y = -3x2 +5x +8
36. (a) x2 = 4py (b) x2 = -4py 37.(a) (x - h)2 = 4p(y - k) (b)(x - h)2 = -4p(y - k) 38. x2 + y2 -2xy - 8xh -8yh = 0
13.
14. (b)
14. (a)
(c)
(d)
15
Exercise Set 1.6
1. -3, 4
2. 3/2, -3
4. -2, 2
5. -3, 0, 3
6. -2, 0, 2
7. -3/2, 0, 3/2, 3
8. 0, 2
9. -3
3. No zeros
16
10. -3, 3
11. 0, 1
12. Even 13. Even 14. Neither 15. Odd 16. Neither 17. Neither 18. Odd 19. Odd 20. Even
21. Odd 22. Even 23. Odd 24. Origin 25. Both 26. y-axis 27. Both 28. Origin 29. Origin
30 (a) violates vertical line test (b) Exercises 25 and
31. (a)
(b)
(c)
(d)
(e)
(f)
17
32. (a)
(b)
(c)
(d)
(e)
(f)
33. (a)
(b)
18
(c)
(d)
(e)
(f)
34. (a)
(b)
(c)
(d)
19
(e)
(f)
37. Yes, also symmetry with respect to the x-axis.
Exercise set 1.7
1. C(3,2) r = 2
2. C(4,2) r = 3
(3, 0)
3. C(-4,3) r =4
(4, -1)
4. C(3,-2) r = 5
(3, -7)
(4,-1)
20
5. C(-1,-4) r = 2
6. C(-3,-2) r = 3
7. C(0,0) r = 2
8. C(0,0) r = 5
9. C(-3,5) r = 5
10. C(1,-2) r = 2
21
11. C(-4,3) r = 4
12. C(3/2,5/2) r = 2
13. C(2/3,-4/3) r = 11/3
14. C(3/2,-1/4) r = 2
15. (2/3,-5/6) r = 3
16. Contradiction 17. Contradiction
18. Contradiction 19. Circle 20. Point
21.Point 22. Contradiction
23. point 24. Point
25. Circle 26 (a) b2 + c2 -4ad > 0 (b) b2 + c2 -4ad = 0 (c) a = 0,
bc =/ 0,
(d) b2 + c2 -4ad < 0 27. (a)
(a)
(b)
(c)
(b) 4 (c)
31. (a)
28. (a) -
(b) -4 (c) -
(b)
(c) 8 (d) 2
22
29. (a)
(b)
(c)
30.
32.
33. (a) y = 5/12x+169/12 (b)the y-values on the tangent line and on
the circle near the point of tangency are almost the same point of.
34. (a) y = 3/4x -25/4 (b) the y-values on the tangent line and on the
circle near the tangency are almost the same.
35. (a) y =12/5x -169/5(b) the y-values on the tangent line and on
the circle near the point of tangency are almost the same
(c)
(a)
36.
37.
(b)
(d) They are translations
38.
41.
39.
40.
42. (a)
(b)
43.
44.
23
(c)
(d)
Exercise Set 1.8
1. (a) Demand, x = 16, p = 4
2. (a) Supply, p = 8
3. (a) Demand, x =12, p = 6
4. (a) Demand, x = 110/7, p = 21
5. (a) Supply, p = 40
6. (a) Supply, p = 10
24
7. (a) Demand x =
p=4
8.
2p +x -300 = 0
Demand
Supply
8p -x -200 = 0
(c) (200, 50), (d) R(x) =-½x2 + 150x
(e) 10,000
9.
10.
-7p + 2x +7 = 0
p +14x -490 = 0
Demand
Supply
Supply
-5p + 2x + 70 = 0
Demand
(c) (105/4, 94) (d) R(x) =-14/5x2 + 98x (e) 2,444
(c) (7, 3) (d) R(x) =
11.
12.
(e) 21
x2 +8x +220 -11p = 0
Supply
Supply
Demand
(c) (11, 5) (d) R(x) =
(e) 55
Demand
x2 +6x -384 +12p = 0
(c) (5.491, 26.742),
(d) R(x) -1/12(x3 +6x2 -84x), (e) 146.84
13. (a) $40 (b)$65 (c) Perhaps everyone has a radio.
14. (a) 60 cords (b) $25 15. 2x -5p + 15 = 0
16. 7x -600p +2400 = 0 17. x + 500p = 20000 18. p= -20/3x + 80, x = -3/20p + 12
25
19. p = -1.5x +110, 73.33 million, which would exceed population of NYC (and capacity of system)
20. (13/4, 107/8) 21. (140/9, 760/9) 22. (2, 9)
23. (50, 350) 24. (17/3, 35/3) 25. (3, 48)
26. 2x + 4p = 21 27. $4800 28. (a) 2300 (b) 120,000
(c) 196 (d)
(e) 120 (f) 1.5, 2297.75
29. (a) 5040 (b) 99.18 (c)
(d) 100.80
(e) 4.5, 894 30. (a) R = -20x2 + 1000x (b) 0 # x # 50
(c) $220 (d) 25, $12,500 31. (a)
(b) 0 # x # 400 (c) 35.73 (d) 267, 11940 32. 345, $345
33. (a)
(c) 4 (d) 10
34.
Chapter One Summary
1.
2.
y=4
x = -2
x=4
y=-1
3.
4. y = -½ x -3 5. (a) (7/2, 0), (0, -7/3)
(b)
6. y = -5/4x - ½
7. 2x -3y = 6 8. (a) 3x - 4y = 17 (b) 4x + 3y = 6
9. No, same x corresponds to different y
10. (a) -5/3 (b) 7 (c) 3
11. (a)
(b)
(c) 3/2, -4/3 (d) -2, 3/2 12. (a) 9 + 2h (b) 5 + 2h (c) 4x + 2h -3 (d) same as before.
26
13. (a) x # 3/4
14. All x except 2/3 and 3/2 15. [-5/2, 3) or (3, 4) or [4, 4)
(b)
(c) y $0
16.
17. 24 18. 105
19. (a) The first is a supply and the second a demand function (b) [2, 8] (c) (5,
21. x =/ 3
) 20. (a) $790 (b) $330
22. NA = not available
x
-2
-1
0
1
2
3
4
5
f(x)
3
4
-2
-3
1
4
7
9
(a)
f(x-2)
NA
NA
3
4
-2
-3
1
4
(b)
f(x+2)
-2
-3
1
4
7
9
NA
NA
(c)
f(x) + 2
5
6
0
-1
3
6
9
11
(d)
f(x) - 4
-1
0
-6
-7
-3
0
3
5
(e)
f(x-2) +3
NA
NA
6
7
1
0
4
7
(f)
f(x+2)+4
2
1
5
8
11
13
NA
NA
23. (a) V(-1,10)
(b) -3.2, 1.2, -1
(c) -2.4, 0.34, -1
26. x2 + y2 -4x +6y - 3 = 0.
24. 50, 100 25. (a) 194 (b) 2x -200 +600/x,
1.94
27. C(2, -3) r = 5
28. C(2, 3) r = 0, it is a point. 29. (a) y = 5/12 x +169/12 (b) on Tan. 11.995833 on Circle 11.995844
27
30.
31.
33. (a)
32.
T
T
T
Note: y-values are positive on (-3, -2.5)
(b) Turning points are indicated in sketch by T.
(There is also one in the interval (-3, -2.5)
34 (a) odd (b) even (c) even (d) odd (e) even
35. (a)
(b)
(c)
28