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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Select from the list of numbers all that belong to the specified set.
1)
Integers
7, , -15, 0, ,
1)
_______ A)
7, 0,
B)
7, -15, 0, ,
C)
7, -15, 0
D)
7, 0 Answer:
B
2)
Natural numbers
16, , -2, 0, ,
2)
_______ A)
16, 0
B)
16,
C)
16, 0,
D)
16, 0, Answer:
B
3)
Real numbers
17, , -7, 0, , ,
3)
_______ A)
17, -7, 0,
B)
17, -7, 0, , C)
17, -7, 0, ,
D)
17, , -7, 0, , Answer:
D
4)
Rational numbers
2, , -17, 0, , , , 0.89
4)
_______ A)
2, -17, 0, , , 0.89
B)
2, 0, C)
, , 0.89
D)
, Answer:
A
5)
Irrational numbers
14, , -18, 0, , , , 0.88
5)
_______ A)
,
B)
, , 0.88
C)
D)
, Answer:
C
6)
Rational numbers-8, 0.7 × , 4 , 2.7, 0.71, 0.
6)
_______ A)
-8, 0.7 × , 2.7, 0. , 0.71
B)
4 C)
4 , 0.71, 0.
D)
-8, 0.7 × , 4 , 2.7, 0.71 Answer:
A
7)
Irrational numbers-6, 6.5 × , 5 , 2.4, 1.4, 0.
7)
_______ A)
5
B)
5 , 0. C)
5 , 1.4, 0.
D)
-6, 6.5 × , 0. , 1.4 Answer:
A
For the measured quantity, state the set of numbers that is most appropriate to describe it. Choose from the natural numbers, integers, or rational numbers.
8)
Populations of cities
8)
_______ A)
Integers
B)
Natural numbers
C)
Rational numbers Answer:
B
9)
Hat sizes
9)
_______ A)
Integers
B)
Rational numbers
C)
Natural numbers Answer:
B
10)
Temperatures given in a winter weather forecast in Alaska
10)
______ A)
Natural numbers
B)
Integers
C)
Rational numbers Answer:
B
11)
Temperatures given in a weather forecast in Cayembe, Equador (this town is on the equator)
11)
______ A)
Rational numbers
B)
Natural numbers
C)
Integers Answer:
B
12)
Numbers of sales of cakes at a bakery
12)
______ A)
Integers
B)
Rational numbers
C)
Natural numbers Answer:
C
13)
The lengths of randomly cut pieces of string (measured using a ruler)
13)
______ A)
Integers
B)
Rational numbers
C)
Natural numbers Answer:
B
14)
The populations of armies of termites living in the walls of houses
14)
______ A)
Rational numbers
B)
Natural numbers
C)
Integers Answer:
B
15)
The lengths of randomly cut pieces of string measured to the nearest inch
15)
______ A)
Rational numbers
B)
Integers
C)
Natural numbers Answer:
C
16)
The average speeds of race cars for one lap at Wilmot Speedway
16)
______ A)
Rational numbers
B)
Natural numbers
C)
Integers Answer:
A
17)
The number of cars sold in an average month at Bob's Auto Sales
17)
______ A)
Integers
B)
Rational numbers
C)
Natural numbers Answer:
C
Write the number in scientific notation. 18)
7,800,000
18)
______ A)
7.8 × 10-5
B)
7.8 × 106
C)
7.8 × 105
D)
7.8 × 10-6 Answer:
B
19)
0.000 259
19)
______ A)
2.59 × 10-5
B)
2.59 × 10-4
C)
2.59 × 104
D)
2.59 × 10-3 Answer:
B
20)
86,000
20)
______ A)
8.6 × 103
B)
8.6 × 10-3
C)
8.6 × 104
D)
8.6 × 10-4 Answer:
C
21)
1 900
21)
______ A)
1. 9 ×
B)
1. 9 ×
C)
1. 9 ×
D)
1. 9 × Answer:
A
22)
0.000000 8
22)
______ A)
8 ×
B)
8 ×
C)
8 ×
D)
8 × Answer:
D
Write the number in standard form. 23)
3.94 × 103
23)
______ A)
39,400
B)
394
C)
3940
D)
118.2 Answer:
C
24)
1.388 × 104
24)
______ A)
138,800
B)
55.52
C)
1388
D)
13,880 Answer:
D
25)
2.0550 × 105
25)
______ A)
20,550
B)
205,500
C)
102.75
D)
2,055,000 Answer:
B
26)
6. 61 × 10-4
26)
______ A)
0.000 6 61
B)
-6 61,000
C)
0.0000 6 61
D)
0.00 6 61 Answer:
A
27)
9. 574 × 10-5
27)
______ A)
0.00000 9 574
B)
0.000 9 574
C)
-9 57,400
D)
0.0000 9 574 Answer:
D
28)
2. 493 × 10-6
28)
______ A)
-2, 493,000
B)
0.0000 2 493
C)
0.00000 2 493
D)
0.000000 2 493 Answer:
C
29)
8. 0 698 × 10-7
29)
______ A)
0.0000000 8 0 698
B)
0.00000 8 0 698
C)
0.000000 8 0 698
D)
-8 0 6, 980,000 Answer:
C
Use a calculator to approximate the expression. Write your answer in scientific notation, and round to the nearest tenth as needed.
30)
( 2.6 × )( 2.2 × )
30)
______ A)
5.7 ×
B)
5.7 ×
C)
57 ×
D)
57 × Answer:
A
31)
31)
______ A)
9.6 ×
B)
9.2 ×
C)
9.2 ×
D)
8.8 × Answer:
C
32)
( 2.8 × ) + ( 2 × )
32)
______ A)
2.2 ×
B)
2.0 ×
C)
2.0 ×
D)
2.2 × Answer:
C
Use a calculator to evaluate the expression. Round your answer to the nearest thousandth. 33)
33)
______ A)
5.602
B)
4.002
C)
2.302
D)
3.302 Answer:
D
34)
34)
______ A)
8.124
B)
9.111
C)
5.653
D)
9.148 Answer:
A
35)
| 9 - |
35)
______ A)
-0.87
B)
0.87
C)
-2.881
D)
2.882 Answer:
B
36)
36)
______ A)
-0.128
B)
-0.141
C)
-0.119
D)
-0.198 Answer:
D
37)
2.6 ( ) - 2 ( 8.8 ) + 6
37)
______ A)
28.096
B)
22.096
C)
16.096
D)
-50.904 Answer:
B
Find the percent change if a quantity changes from to . Round your answer to the nearest tenth if appropriate.
38)
= $ 10, = $ 52
38)
______ A)
-80.8
B)
80.8
C)
420
D)
-420 Answer:
C
39)
= 5.3, = 2.4
39)
______ A)
54.7
B)
-120.8
C)
120.8
D)
-54.7 Answer:
D
Use the information given in the table to solve the problem. 40)
The table gives the Consumer Price Index for selected years.
What is the percent change (to the nearest tenth of a percent) in prices from 1965 to 1980?
40)
______ A)
125.3 %
B)
225.7 %
C)
124.1 %
D)
127.6 % Answer:
A
41)
The table gives the Consumer Price Index for selected years.
What is the percent change (to the nearest tenth of a percent) in prices from 1960 to 1975?
41)
______ A)
137.3 %
B)
141.5 %
C)
138.5 %
D)
147.3 % Answer:
A
42)
The table gives the Consumer Price Index for selected years.
Use the concept of an average or mean to estimate the CPI in 1961.
42)
______ A)
34
B)
33.1
C)
30.7
D)
34.6 Answer:
B
43)
The table gives the Consumer Price Index for selected years.
Use the concept of an average or mean to estimate the CPI in 1965.
43)
______ A)
54.8
B)
57.9
C)
55.5
D)
53.2 Answer:
A
44)
The table gives the value of a 1957 Chevy BelAire in #2 condition for selected years.
What is the percent change (to the nearest tenth of a percent) in the value of a 1957 Chevy BelAir in #2 condition from 1982 to 1986.
44)
______ A)
21.5 %
B)
25.2 %
C)
30.5 %
D)
26.1 % Answer:
B
45)
The table gives the value of a 1957 Chevy BelAire in #2 condition for selected years.
Use the concept of an average or mean to estimate the value of a 1957 ChevyBelAire in #2 condition in 1983.
45)
______ A)
$ 9210.00
B)
$ 9239.13
C)
$ 9200.00
D)
$ 9180.87 Answer:
A
46)
The table gives the value of a 1957 Chevy BelAire in #2 condition for selected years.
What is the percent change (to the nearest tenth of a percent) in the value of a 1957 Chevy BelAir in #2 condition from 1982 to 1988?
46)
______ A)
47 %
B)
49.1 %
C)
47.5 %
D)
53.4 % Answer:
B
47)
The table gives the value of a 1957 Chevy BelAire in #2 condition for selected years.
Use the concept of an average or mean to estimate the value of a 1957 ChevyBelAire in #2 condition in 1985.
47)
______ A)
$ 10,237.78
B)
$ 10,272.57
C)
$ 10,261.50
D)
$ 10,265.73 Answer:
C
Solve. Write results using scientific notation. 48)
Assume that the volume of the earth is 3.8 x 1014 cubic meters and the volume of a bacterium is 3.0 x 10-16 cubic meters. If the earth could be filled with bacteria, how many would it contain?
48)
______ A)
1.27 x 10-30 bacteria
B)
1.27 x 1031 bacteria C)
1.27 x 10-31 bacteria
D)
1.27 x 1030 bacteria Answer:
D
49)
A computer can do one calculation in 1.8 x 10-7 seconds. How long would it take the computer to do a trillion (1012) calculations?
49)
______ A)
1.8 x 106 sec
B)
1.8 x 10-7 sec
C)
1.8 x 1012 sec
D)
1.8 x 105 sec Answer:
D
50)
The national debt of a small country is $ 7,120,000,000 and the population is 2,473,000. What is the amount of debt per person?
50)
______ A)
$ 28.79 x 102
B)
$ 2.88 x 103
C)
$ 2.88 x 106
D)
$ 2.88 Answer:
B
51)
A company produced 956,000 small appliances in one year and made a profit of . What was the profit on each appliance?
51)
______ A)
$ 6.05
B)
$ 6.05 x 10-1
C)
$ 1.65 x 10-1
D)
$ 1.65 x 101 Answer:
A
52)
The earth is approximately 92,900,000 miles from the sun. If what is the distance to the sun in meters?
52)
______ A)
1.50 x 1011 m
B)
5.7 x 1010 m
C)
1.50 x 1010 m
D)
5.7 x 10-10 m Answer:
A
53)
The distance from the earth to the sun is 92,900,000 miles. How long would it take a rocket, traveling at 2.9 x 103 miles per hour, to reach the sun?
53)
______ A)
3.2 x 102 hr
B)
3.2 x 103 hr
C)
3.2 hr
D)
3.2 x 104 hr Answer:
D
54)
A light-year is the distance that light travels in one year. Find the number of miles in a light-year if light travels 1.86 x 105 miles per second.
54)
______ A)
5.9 x 107 miles
B)
5.9 x 1014 miles
C)
5.9 x 1012 miles
D)
5.9 x 105 miles Answer:
C
55)
The following equation gives the number of atoms in 240 g of fluorine. How many atoms are there?
A = 240 g Fl x x
55)
______ A)
4.77 x 1024 atoms
B)
2.75 x 1026 atoms C)
7.6 x 1024 atoms
D)
7.61 x 1024 atoms Answer:
D
Solve the problem. 56)
A comet has a nearly circular orbit around a star with a radius of 345 million miles and requires 8.72 earth years to complete one orbit. Estimate the orbital speed of the comet in miles per hour. Round to the nearest mile per hour.
56)
______ A)
681,067 mph
B)
248,589,329 mph C)
249 mph
D)
28,378 mph Answer:
D
57)
An oil spill of 3676 cubic centimeters is spilled onto a pond and spreads out in a circular shape having a diameter of 428 centimeters. Approximate the thickness of the oil film to four decimal places.
57)
______ A)
0.0256 cm
B)
39.1383 cm
C)
5.4678 cm
D)
2.7339 cm Answer:
A
Plot each number on a number line. 58)
-2.5, 2, 4, -2
58)
______ A)
B)
C)
D)
Answer:
C
59)
0.6, -0.8, 1, 0
59)
______ A)
B)
C)
D)
Answer:
B
60)
150, -50, 200, -300
60)
______ A)
B)
C)
D)
Answer:
B
61)
-10, 30, 40, -60
61)
______ A)
B)
C)
D)
Answer:
B
Find the mean of the set of data. Round to the nearest tenth. 62)
5, 16, 8, 5, 11, 8, 15, 16, 17
62)
______ A)
11.1
B)
10.8
C)
11.3
D)
11.2 Answer:
D
63)
93, 45, 4, 40, 76, 24, 74, 109, 12
63)
______ A)
51.7
B)
53.0
C)
59.6
D)
44.6 Answer:
B
64)
4, 11, 15, 4, 4, 15, 15, 15, 15, 11, 15, 11, 15
64)
______ A)
11.5
B)
11.8
C)
12.5
D)
11.6 Answer:
A
65)
85, 41, 58, 58, 41, 85, 13, 13, 13, 85, 13, 13, 58
65)
______ A)
46.9
B)
43.1
C)
44.3
D)
43.2 Answer:
C
66)
230, 220, 213, 213, 213, 213, 220, 216, 216, 216, 220, 220
66)
______ A)
217.5
B)
217.6
C)
217.3
D)
218.5 Answer:
A
67)
0, 6, 4, 5, 5, 6, 4, 0, 0, 5, 6, 6
67)
______ A)
4.2
B)
5.2
C)
4.9
D)
3.9 Answer:
D
Find the median of the set of data. 68)
1, 9, 15, 21, 41, 45, 49
68)
______ A)
26
B)
21
C)
41
D)
15 Answer:
B
69)
13, 13, 31, 53, 69, 70, 87
69)
______ A)
31
B)
69
C)
53
D)
48 Answer:
C
70)
56, 22, 207, 134, 257, 236, 232
70)
______ A)
134
B)
232
C)
207
D)
163 Answer:
C
71)
14, 127, 264, 224, 400, 417
71)
______ A)
244
B)
206.5
C)
224
D)
264 Answer:
A
72)
5, 4, 21, 13, 26, 45, 36, 33
72)
______ A)
23.5
B)
22.5
C)
21
D)
26 Answer:
A
73)
38, 15, 9, 9, 26, 12, 29, 38, 39, 34
73)
______ A)
27.5
B)
29
C)
25
D)
26 Answer:
A
Find the distance in the xy-plane between the two points. Round an approximate result to the nearest hundredth.
74)
( 8, 0) and (0, 6)
74)
______ A)
3.16
B)
20
C)
10
D)
2 Answer:
C
75)
( 4, 7) and ( 9, 19)
75)
______ A)
12
B)
13
C)
3.46
D)
5 Answer:
B
76)
( -2, 2) and ( -10, -4)
76)
______ A)
3.16
B)
10
C)
-10
D)
24 Answer:
B
77)
( -3, 1) and ( 1, -5)
77)
______ A)
7.21
B)
6.93
C)
24
D)
26 Answer:
A
78)
(- 6, -2) and (0, -20)
78)
______ A)
18.97
B)
30
C)
9.485
D)
9 Answer:
A
79)
( 7.3, 1.4) and ( 1.3, 7.4)
79)
______ A)
12
B)
16.97
C)
8.49
D)
1.41 Answer:
C
80)
( 4.8, -0.7) and ( 2.8, -4.7)
80)
______ A)
2.24
B)
4.47
C)
8.94
D)
4 Answer:
B
Find the midpoint of the line segment joining the two points. 81)
( 2, 2) and ( 9, 0)
81)
______ A)
B)
C)
D)
Answer:
B
82)
( 2, -6) and ( -5, 3)
82)
______ A)
B)
C)
D)
Answer:
A
83)
( -4, -1) and ( 7, 4)
83)
______ A)
B)
C)
D)
Answer:
B
84)
( 7, -4) and ( -3, 4)
84)
______ A)
B)
C)
D)
Answer:
D
85)
and
85)
______ A)
B)
C)
D)
Answer:
D
86)
( 7 , - ) and (- , 0)
86)
______ A)
B)
( -5, 11)
C)
D)
Answer:
A
87)
(- , 1) and (0, )
87)
______ A)
B)
C)
( - , 1 + )
D)
Answer:
B
Find the domain and range of the relation. 88)
{( -8, -5), ( 12, 1), ( -9, -8), ( -6, -1), ( 3, 7)}
88)
______ A)
D = { -6, 12, -9, 3, -8}; R = { -1, 1, -8, 7, -5}
B)
D = { -6, -1, 12, 1, -9}; R = { -8, 3, 7, -8, -5} C)
D = { -1, 1, -8, 7, -5}; R = { -6, 12, -9, 3, -8}
D)
D = { -8, 3, 7, -8, -5}; R = { -6, -1, 12, 1, -9} Answer:
A
89)
{( 8, 1), ( 11, -4), ( -6, 5), ( -6, 4)}
89)
______ A)
D = { 8, -6, 11}; R = { 1, 5, -4, 4}
B)
D = { 8, -6, 11, -6}; R = { 1, 5, -4, 4} C)
D = { 8, -6, 11, 6}; R = { 1, 5, -4, 4}
D)
D = { 1, 5, -4, 4}; R = { 8, -6, 11} Answer:
A
90)
{( -9, 4), ( -9, 6), ( 9, 5), ( 5, -7), ( 3, 9)}
90)
______ A)
D = { 3, -5, 9, -9, 5}; R = { 9, 5, 6, -7, 4}
B)
D = { 3, 9, -9, 5}; R = { 9, 5, 6, -7, 4} C)
D = { 9, 5, 6, -7, 4}; R = { 3, 3, 9, -9, 5}
D)
D = { 3, 3, 9, -9, 5}; R = { 9, 5, 6, -7, 4} Answer:
B
91)
{( 9, -1), ( -6, 1), ( 12, 5), ( 12, 6)}
91)
______ A)
D = { -6, 12, 9}; R = { 1, 5, -1, 6}
B)
D = { 1, 5, -1, 6}; R = { -6, 12, 9} C)
D = { -6, 12, 9, 12}; R = { 1, 5, -1, 6}
D)
D = { -6, 12, 9, -12}; R = { 1, 5, -1, 6} Answer:
A
92)
{( -3, -3), ( -5, 7), ( 1, -4), ( 7, -9)}
92)
______ A)
D = { 1, 7, -3, -5}; R = { -4, -4, -9, -3, 7}
B)
D = { -4, -9, -3, 7}; R = { 1, 7, -3, -5} C)
D = { 1, 7, -3, -5}; R = { -4, 3, -9, -3, 7}
D)
D = { 1, 7, -3, -5}; R = { -4, -9, -3, 7} Answer:
D
93)
{( -77, -91), ( -21, -78), ( -12, -53), ( 27, -17), ( 69, 52)}
93)
______ A)
D = { -77, -21, -12, 27}; R = { -91, -78, -53, -17} B)
D = { -77, -21, -12, 27, 69}; R = { -91, -78, -53, -17, 52} C)
D = { -91, -78, -53, -17}; R = { -77, -21, -12, 27} D)
D = { -91, -78, -53, -17, 52}; R = { -77, -21, -12, 27, 69} Answer:
B
94)
{( -11.16, -8.54), ( -9.71, -5.92), ( -3.34, -4.25), ( 3.68, -0.41), ( 13.78, 4.16)}
94)
______ A)
D= { -8.54, -5.92, -0.41, 4.16}; R = { -11.16, -9.71, -3.34, 3.68} B)
D = { -8.54, -5.92, -4.25, -0.41, 4.16}; R = { -11.16, -9.71, -3.34, 3.68, 13.78} C)
D = { -11.16, -9.71, 3.68, 13.78}; R= { -8.54, -5.92, -4.25, -0.41} D)
D = { -11.16, -9.71, -3.34, 3.68, 13.78}; R = { -8.54, -5.92, -4.25, -0.41, 4.16} Answer:
D
Plot the relation in the xy-plane. 95)
{(0, 3), (-3, -2), (4, 1), ( -6, -10), (-1, 6)}
95)
______ A)
B)
C)
D)
Answer:
C
96)
{(10, 35), (-35, -20), (40, 15), ( -89, -20), (-10, 75)}
96)
______ A)
B)
C)
D)
Answer:
C
97)
{(0.4, 1.3), (-1.3, -1.2), (1.4, -0.1), ( 0.7, -0.5), (-1, 0.5)}
97)
______ A)
B)
C)
D)
Answer:
C
98)
{(0, 3), ( 6, -7), (4, 1), ( -5, -10), (-1, 7)}
98)
______ A)
B)
C)
D)
Answer:
B
99)
{(10, 35), ( -20, -70), (40, 15), ( -61, -20), (-10, 55)}
99)
______ A)
B)
C)
D)
Answer:
C
100)
{(0.4, 1.3), ( -1.1, 0.3), (1.4, -0.1), ( 0.7, -0.5), (-1, 0.5)}
100)
_____ A)
B)
C)
D)
Answer:
C
101)
{(0, -6), ( 6, 8), ( 9, 0), ( -9, -10), (-1, 6)}
101)
_____ A)
B)
C)
D)
Answer:
A
102)
{(0, -75), ( -48, 17), ( 17, 0), ( -60, -20), (-10, 61)}
102)
_____ A)
B)
C)
D)
Answer:
C
103)
{(0, 0.7), ( 0.8, -0.4), ( -0.4, 0), ( 0.8, -0.5), (-1, 0.6)}
103)
_____ A)
B)
C)
D)
Answer:
D
Make a scatterplot of the data. 104)
{( -5, 7),( -6, -2),( -5, -2),( -6, -8),( -9, 2),( 3, -2),( -1, 2),( 8, 3),( -4, -9),( -2, -3)}
104)
_____ A)
B)
C)
D)
Answer:
B
105)
{( 0.7, 0.67),( 0.18, 0.92),( 0.46, 0.74),( 0.17, 0.14),( -0.09, -0.95),( 0.96, 0.64),( 0.81, 0.22),( 0.39, 0.26)}
105)
_____ A)
B)
C)
D)
Answer:
B
106)
{( 16, 63),( -8, 30),( 12, 39),( -15, -10),( 4, -1),( 9, 36),( 7, 9),( 15, 62),( 7, 7),( -3, 4)}
106)
_____ A)
B)
C)
D)
Answer:
D
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Make a line graph of the data.
107)
The following table shows the average tuition for one semester at City X College over various years. Use time on the horizontal scale for your line graph.
107)
____________ Answer:
Answers may vary. A possible answer follows.
108)
The following table shows the number of computer sales made at Computer Buy over five months. Use time on the horizontal scale for your line graph.
108)
____________ Answer:
Answers may vary. A possible answer follows.
109)
The following table shows the median teacher's salary in District X over several years. Use time on the horizontal scale for your line graph.
109)
____________ Answer:
Answers may vary. The following is a possible answer.
110)
The following table gives the average cost of producing a music video over the given years. Use time on the horizontal scale for your line graph.
110)
____________ Answer:
Answers may vary. A possible answer follows.
111)
The following table gives the total amount of precipitation during the given months. Use time on the horizontal scale for your line graph.
111)
____________ Answer:
Answers may vary. A possible answer follows.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the center and radius of the circle.
112)
+ = 49
112)
_____ A)
Center: (0, 0), radius: 7
B)
Center: (1, 1), radius: 7 C)
Center: (0, 0), radius: 49
D)
Center: (1, 1), radius: 49 Answer:
A
113)
+ = 26
113)
_____ A)
Center: (1, 1), radius:
B)
Center: (1, 1), radius: 26 C)
Center: (0, 0), radius: 26
D)
Center: (0, 0), radius: Answer:
D
114)
(x + 6)2 + (y - 2)2 = 16
114)
_____ A)
Center: ( -6, 2), radius = 4
B)
Center: ( 6, -2), radius = 16 C)
Center: ( -2, 6), radius = 16
D)
Center: ( 2, -6), radius = 4 Answer:
A
115)
x2 + (y + 4)2 = 81
115)
_____ A)
Center: ( -4, 0), radius = 9
B)
Center: (0, -4), radius = 81 C)
Center: (0, -4), radius = 9
D)
Center: (0, 4), radius = 9 Answer:
C
116)
(x - 7)2 + y2 = 16
116)
_____ A)
Center: ( -7, 0), radius = 4
B)
Center: ( 7, 0), radius = 16 C)
Center: ( 7, 0), radius = 4
D)
Center: (0, 7), radius = 4 Answer:
C
117)
7 + 7 = 49
117)
_____ A)
Center: (0, 0), radius: 7
B)
Center: (0, 0), radius: C)
Center: ( 7, 7), radius:
D)
Center: (0, 0), radius: 49 Answer:
B
118)
x2 + 12x + 36 + y2 + 18y + 81 = 64
118)
_____ A)
( -6, -9), r = 8
B)
( -9, -6), r = 8
C)
( 9, 6), r = 64
D)
( 6, 9), r = 64 Answer:
A
119)
x2 + y2 - 6x + 8y + 25 = 4
119)
_____ A)
( 4, -3), r = 4
B)
( -4, 3), r = 2
C)
( -3, 4), r = 4
D)
( 3, -4), r = 2 Answer:
D
120)
x2 + y2 - 16x + 2y = -56
120)
_____ A)
( -1, 8), r = 3
B)
( -8, 1), r = 9
C)
( 8, -1), r = 3
D)
( 1, -8), r = 9 Answer:
C
121)
x2 + y2 = 8x + 9
121)
_____ A)
( -4, 0), r = 25
B)
( 4, 0), r = 25
C)
( -4, 0), r = 5
D)
( 4, 0), r = 5 Answer:
D
122)
x2 + 12x + y2 + 4y - 24 = 0
122)
_____ A)
( -6, -2), r = 8
B)
( 6, 2), r = 64
C)
( 6, 2), r = 8
D)
( -6, -2), r = 64 Answer:
A
Use the graph to find the standard equation of the circle. 123)
123)
_____ A)
+ = 6
B)
+ = 12
C)
+ = 16
D)
+ = 36 Answer:
D
124)
124)
_____ A)
+ = 36
B)
+ = 6 C)
+ = 6
D)
+ = 36 Answer:
D
125)
125)
_____ A)
+ = 36
B)
+ = 36 C)
+ = 6
D)
+ = 6 Answer:
B
126)
126)
_____ A)
+ = 6
B)
+ = 36 C)
+ = 36
D)
+ = 36 Answer:
B
127)
127)
_____ A)
+ = 36
B)
+ = 36 C)
+ = 36
D)
+ = 6 Answer:
C
Find the standard equation of the circle that satisfies the conditions. 128)
Center ( 3, 7), radius 4
128)
_____ A)
+ = 16
B)
+ = 4 C)
+ = 4
D)
+ = 16 Answer:
A
129)
Center ( -9, -7), radius
129)
_____ A)
+ = 11
B)
+ = 121 C)
+ = 11
D)
+ = 121 Answer:
C
130)
Center ( 6, 0), radius 9
130)
_____ A)
+ = 81
B)
+ = 9 C)
+ = 9
D)
+ = 81 Answer:
A
131)
Center (0, 0), radius 7
131)
_____ A)
+ = 49
B)
+ = C)
+ = 7
D)
+ = 49 Answer:
A
132)
Center ( -6, 1) with the point ( -3, 5) on the circle
132)
_____ A)
+ = 25
B)
+ = 9 C)
+ = 25
D)
+ = 9 Answer:
A
133)
Endpoints of a diameter ( -5, 4) and ( 3, 2)
133)
_____ A)
+ = 17
B)
+ = 40 C)
+ = 68
D)
+ = 8 Answer:
A
Provide the requested response. 134)
For the viewing rectangle [-14, 14, 2] by [-10, 10, 2] , state the number of tick marks on the positive x-axis.
134)
_____ A)
10
B)
5
C)
14
D)
7 Answer:
D
135)
For the viewing rectangle [0, 10, 2] by [0, 22, 2] , state the number of tick marks on the positive y-axis.
135)
_____ A)
11
B)
10
C)
22
D)
5 Answer:
A
136)
For the viewing rectangle [ -40, 40, 5] by [0, 20, 5] , state the number of tick marks on the positive x-axis.
136)
_____ A)
8
B)
10
C)
6
D)
13 Answer:
A
137)
For the viewing rectangle [1970, 2050, 10] by [13,000, 23,000, 1000] , state the number of tick marks on the positive x-axis.
137)
_____ A)
11
B)
9
C)
6
D)
16 Answer:
B
138)
For the viewing rectangle [1970, 2040, 10] by [13,000, 25,000, 1000] , state the number of tick marks on the positive y-axis.
138)
_____ A)
15
B)
8
C)
13
D)
19 Answer:
C
139)
Choose the correct viewing rectangle to match the settings: by .
139)
_____ A)
B)
C)
D)
Answer:
D
140)
Choose the correct viewing rectangle to match the settings: by
140)
_____ A)
B)
C)
D)
Answer:
D
141)
Choose the correct viewing rectangle to match the settings: by
141)
_____ A)
B)
C)
D)
Answer:
A
142)
Choose the correct viewing rectangle to match the settings: [ -2 , 10 , 1 ] by
142)
_____ A)
B)
C)
D)
Answer:
B
143)
Choose the correct viewing rectangle to match the settings: [ -2 , 10 , 2 ] by
143)
_____ A)
B)
C)
D)
Answer:
C
144)
If f( 10) = -4 identify a point on the graph of f.
144)
_____ A)
( 10, -4)
B)
( 10, 4)
C)
(-10, -4)
D)
( -4, 10) Answer:
A
145)
If the point ( -9, 8.8) lies on the graph of f, then f( __ ) = ___ .
145)
_____ A)
f(0) = 8.8
B)
f( -9) = 0
C)
f( -9) = 8.8
D)
f( 8.8) = -9 Answer:
C
Graph f by hand by first plotting points to determine the shape of the graph. 146)
f(x) = -3x + 6
146)
_____ A)
B)
C)
D)
Answer:
A
147)
f(x) = x - 4
147)
_____ A)
B)
C)
D)
Answer:
D
148)
f(x) = -5x
148)
_____ A)
B)
C)
D)
Answer:
D
149)
f(x) = x + 1
149)
_____ A)
B)
C)
D)
Answer:
A
150)
f(x) = x
150)
_____ A)
B)
C)
D)
Answer:
D
151)
f(x) = -6
151)
_____ A)
B)
C)
D)
Answer:
C
152)
f(x) =
152)
_____ A)
B)
C)
D)
Answer:
C
153)
f(x) =
153)
_____ A)
B)
C)
D)
Answer:
A
154)
f(x) =
154)
_____ A)
B)
C)
D)
Answer:
A
155)
f(x) = -2x2
155)
_____ A)
B)
C)
D)
Answer:
A
Evaluate the function as indicated. 156)
Find f( 12) when f(x) = -5x - 10.
156)
_____ A)
-50
B)
-70
C)
-61
D)
50 Answer:
B
157)
Find g(a - 1) when g(x) = 5x + 4.
157)
_____ A)
5a - 1
B)
a + 4
C)
5a + 4
D)
5a + 1 Answer:
A
158)
Find f( 5.3) when f(x) = 19.
158)
_____ A)
19
B)
-19
C)
5.3
D)
100.7 Answer:
A
159)
Find f( 4) when f(x) = x2 + 3x - 4.
159)
_____ A)
0
B)
32
C)
24
D)
8 Answer:
C
160)
Find f(k - 1) when f(x) = 5x2 + 5x - 6.
160)
_____ A)
5k2 - 25k + 4
B)
-5k2 + 5k - 6
C)
5k2 - 5k - 6
D)
5k2 - 5k + 4 Answer:
C
161)
Find f( 8) when f(x) = .
161)
_____ A)
B)
C)
D)
Answer:
B
162)
Find f(t + 2) when f(x) = .
162)
_____ A)
B)
C)
D)
Answer:
A
163)
Find f( -9) when f(x) = .
163)
_____ A)
B)
C)
-
D)
Answer:
A
Specify the domain of the function. 164)
f(x) = -2x - 1
164)
_____ A)
All real numbers
B)
x > 0 C)
x ≠ 0
D)
x ≥ 1 Answer:
A
165)
f(x) = 4x2 + 8x + 8
165)
_____ A)
x < 0
B)
x > 0 C)
All real numbers
D)
x ≠ 0 Answer:
C
166)
f(x) =
166)
_____ A)
x ≠ 17
B)
x ≤ 17 C)
All real numbers
D)
x > Answer:
B
167)
f(x) =
167)
_____ A)
x > 36
B)
x ≠ 36 C)
All real numbers
D)
x ≠ 6, x ≠ -6 Answer:
D
168)
f(x) =
168)
_____ A)
x > 0
B)
x ≠ 2 C)
All real numbers
D)
x ≠ -2 Answer:
B
169)
f(x) =
169)
_____ A)
All real numbers
B)
x ≠ 9, x ≠ -9 C)
x > 81
D)
x ≠ 81 Answer:
A
170)
f(x) =
170)
_____ A)
All real numbers
B)
x > 0 C)
x ≥ -5, x ≠ -1, x ≠ 6
D)
x ≠ -5, x ≠ -1, x ≠ 6 Answer:
C
171)
f(x) = -3
171)
_____ A)
All real numbers
B)
x ≠ -3 C)
x ≥ 0
D)
x = -3 Answer:
A
Find the domain and the range for the function. 172)
172)
_____ A)
D: , R:
B)
D: , R: C)
D: , R:
D)
D: All real numbers, R: All real numbers Answer:
D
173)
173)
_____ A)
D: All real numbers, R: All real numbers
B)
D: , R: C)
D: , R:
D)
D: , R: Answer:
A
174)
174)
_____ A)
D: , R:
B)
D: , R: C)
D: , R:
D)
D: , R: Answer:
A
175)
175)
_____ A)
D: All real numbers, R: B)
D: , R: C)
D: , R: D)
D: , R: Answer:
A
176)
176)
_____ A)
D: All real numbers, R: B)
D: , R: C)
D: , R: D)
D: , R: Answer:
C
177)
177)
_____ A)
D: , R: All real numbers B)
D: All real numbers, R: All real numbers C)
D: , R: D)
D: , R: Answer:
D
178)
178)
_____ A)
D: , R: B)
D: , R: C)
D: , R: D)
D: All real numbers, R: All real numbers Answer:
C
179)
179)
_____ A)
D: , R:
B)
D: , R: C)
D: , R:
D)
D: , R: Answer:
D
180)
180)
_____ A)
D: , R:
B)
D: , R: C)
D: , R:
D)
D: All real numbers, R: All real numbers Answer:
D
Use the graph to evaluate the function value. 181)
f( 2)
181)
_____ A)
2
B)
0
C)
4
D)
-2 Answer:
B
For the given function expressed verbally, give a graphical representation. 182)
To convert x inches to y centimeters, multiply x by 2.54. Let y = f(x) and 0≤x≤50.
182)
_____ A)
B)
C)
D)
Answer:
A
183)
To convert x centimeters to y inches, divide x by 2.54. Let y = f(x) and 0≤x≤15.
183)
_____ A)
B)
C)
D)
Answer:
D
184)
To convert x square yards to y square feet, multiply x by 9. Let y = f(x) and
184)
_____ A)
B)
C)
D)
Answer:
D
185)
To convert x square feet to y square yards, divide x by 9. Let y = f(x) and 0≤x≤100.
185)
_____ A)
B)
C)
D)
Answer:
D
186)
Surveyors use the "link" as a unit of measure. To convert x links to y inches, multiply x by 7.92. Let and 0≤x≤10.
186)
_____ A)
B)
C)
D)
Answer:
C
187)
Surveyors use the "link" as a unit of measure. To convert x inches to y links, divide x by 7.92. Let y = f(x) and 0≤x≤100.
187)
_____ A)
B)
C)
D)
Answer:
C
188)
Bob buys a car that gets 13 miles per gallon of gasoline. Give a representation to compute the number of miles, y , that Bob can travel with x gallons of gasoline. Let 0≤x≤10.
188)
_____ A)
B)
C)
D)
Answer:
D
Give a verbal representation for the given function. 189)
f(x) = 3 . Let y = f(x).
189)
_____ A)
To obtain y: Add 3 to x, then square the result. B)
To obtain y: Square x, then multiply the result by 3. C)
To obtain y: Multiply x by 3, then square the result. D)
To obtain y: Square x, then add 3 to the result. Answer:
B
190)
f(x) = 5 x - 2 . Let y = f(x).
190)
_____ A)
To obtain y: Multiply x by 5, then subtract 2 from the result. B)
To obtain y: Divide x by 5, then subtract 2 from the result. C)
To obtain y: Subtract 2 from x, then multiply the result by 5. D)
To obtain y: Multiply x by 2, then subtract 5 from the result. Answer:
A
191)
f(x) = + 19 . Let y = f(x).
191)
_____ A)
To obtain y: Divide x by 3, then add 19 to the result. B)
To obtain y: Multiply x by 3, then add 19 to the result. C)
To obtain y: Multiply x by 19, then divide the result by 3. D)
To obtain y: Add 19 to x, then divide the result by 3. Answer:
A
192)
f(x) = 6 . Let y = f(x).
192)
_____ A)
y is equal to 6 minus x.
B)
y is equal to 6 times x. C)
y is equal to 6 plus x.
D)
y is equal to 6. Answer:
D
193)
f(x) = + 7. Let y = f(x).
193)
_____ A)
To obtain y: Multiply x by -1, then add 7 to the result. B)
To obtain y: Add 7 to x. C)
To obtain y: Add 7 to the opposite of x. D)
To obtain y: If x is positive or equal to zero, add 7 to x. If x is negative, add 7 to the opposite of x. Answer:
D
194)
f(x) = 14 - x. Let y = f(x).
194)
_____ A)
To obtain y: Multiply 14 by -1, then subtract x from the result. B)
To obtain y: Subtract 14 from x. C)
To obtain y: Subtract x from 14. D)
To obtain y: Multiply x by -1, then subtract 14 from the result. Answer:
C
195)
f(x) = 15 - 5x. Let y = f(x).
195)
_____ A)
To obtain y: Add 5 to x, then add 15 to the result. B)
To obtain y: Subtract 5 from 15 , then multiply the result times x. C)
To obtain y: Multiply x by 5, then subtract the result from 15. D)
To obtain y: Multiply x by 15, then subtract the result from 5. Answer:
C
Use the table to solve the problem. 196)
For a function f , we have the following numerical representation.
Evaluate f for x = 1.
196)
_____ A)
0
B)
16
C)
4
D)
8 Answer:
C
197)
For a function f we have the following numerical representation.
Evaluate f for x = -1.
197)
_____ A)
0
B)
6
C)
5
D)
4 Answer:
C
198)
For a function f we have the following numerical representation.
Evaluate f for x = 2.
198)
_____ A)
5
B)
6
C)
4
D)
0 Answer:
B
199)
For a function f we have the following numerical representation.
Evaluate f for x = -1.
199)
_____ A)
-0.18
B)
0.18
C)
-0.09
D)
0.09 Answer:
C
200)
For a function f we have the following numerical representation.
Evaluate f for x = 2.
200)
_____ A)
-0.11
B)
5
C)
-0.22
D)
0.22 Answer:
D
201)
The cost in dollars of driving a certain make and model of car for x miles is given by the function f. A numerical representation of f is given in the following table.
Use the table to evaluate f for x = 3.
201)
_____ A)
$ 1.62
B)
$ 0.54
C)
$3.24
D)
$2.16 Answer:
A
202)
The cost in dollars of driving a certain make and model of car for x miles is given by the function f. A numerical representation of f is given in the following table.
If the cost is $ 2.20, how many miles have been driven?
202)
_____ A)
6 miles
B)
3 miles
C)
5 miles
D)
4 miles Answer:
D
203)
The cost in dollars of driving a certain make and model of car for x miles is given by the function f. A numerical representation of f is given in the following table.
If the cost is $ 1.12, how many miles have been driven?
203)
_____ A)
2 miles
B)
4 miles
C)
3 miles
D)
1 miles Answer:
A
204)
The cost, in dollars, of a cab ride for x miles is given by the function f in the following table.
What is the cost of a 4-mile cab ride?
204)
_____ A)
$ 6.60
B)
$ 4.86
C)
$ 5.73
D)
$ 3.99 Answer:
C
205)
The cost, in dollars, of a cab ride for x miles is given by the function f in the following table.
After 1 mile has been driven, what is the cost of each additional mile?
205)
_____ A)
$ 0.61
B)
$ 0.73
C)
$ 0.76
D)
$ 0.65 Answer:
B
Determine if the relation is a function. 206)
206)
_____ A)
Not a function
B)
Function Answer:
B
207)
207)
_____ A)
Function
B)
Not a function Answer:
A
208)
208)
_____ A)
Function
B)
Not a function Answer:
B
209)
209)
_____ A)
Not a function
B)
Function Answer:
A
210)
210)
_____ A)
Not a function
B)
Function Answer:
B
211)
211)
_____ A)
Function
B)
Not a function Answer:
A
212)
S={( 8, 1), ( 9, 3), ( 16, 0), ( 7, 1), ( -8, -2)}
212)
_____ A)
Not a Function
B)
Function Answer:
B
213)
S={( -20, 19), ( -19, 21), ( -40, 0), ( -21, 19), ( -20, 16)}
213)
_____ A)
Function
B)
Not a Function Answer:
B
214)
214)
_____ A)
Not a Function
B)
Function Answer:
B
215)
215)
_____ A)
Not a Function
B)
Function Answer:
A
Answer the question. 216)
In a gymnasium, a group of 32 students are individually counted off by fours to determine teams; i.e. "1, 2, 3, 4, 1, 2, 3, 4, 1, 2, ..."? Is a function generated by a relation that takes a student's number as input and outputs the students name with that number?
216)
_____ A)
No
B)
Yes Answer:
A
217)
In the equation x = - 10, is y a function of x?
217)
_____ A)
No
B)
Yes Answer:
B
For the given function expressed verbally, give a symbolic representation. 218)
To convert x inches to y centimeters, multiply x by 2.54. Let y = f(x).
218)
_____ A)
f(x) = 2.54/x
B)
f(x) = x - 2.54
C)
f(x) = 2.54x
D)
f(x) = x/2.54 Answer:
C
219)
To convert x centimeters to y inches, divide x by 2.54. Let y = f(x).
219)
_____ A)
f(x) = 2.54 - x
B)
f(x) = 2.54x
C)
f(x) = 2.54/x
D)
f(x) = x/2.54 Answer:
D
220)
To convert x square yards to y square feet, multiply x by 9. Let y = f(x).
220)
_____ A)
f(x) = 9 - x
B)
f(x) = 9/x
C)
f(x) = 9x
D)
f(x) = x/9 Answer:
C
221)
To convert x square feet to y square yards, divide x by 9. Let y = f(x).
221)
_____ A)
f(x) = 9x
B)
f(x) = x/9
C)
f(x) = 9/x
D)
f(x) = x - 9 Answer:
B
222)
Surveyors use the "link" as a unit of measure. To convert x links to y inches, multiply x by 7.92. Let y = f(x).
222)
_____ A)
f(x) = 7.92x
B)
f(x) = x/7.92
C)
f(x) = 7.92/x
D)
f(x) = x + 7.92 Answer:
A
223)
Surveyors use the "link" as a unit of measure. To convert x inches to y links, divide x by 7.92. Let y = f(x).
223)
_____ A)
f(x) = 7.92 - x
B)
f(x) = 7.92/x
C)
f(x) = x/7.92
D)
f(x) = 7.92x Answer:
C
224)
Bob buys a car that gets 9 miles per gallon of gasoline. Give a representation to compute the number of miles, y , that Bob can travel with x gallons of gasoline. Let y = f(x).
224)
_____ A)
f(x) = 9/x
B)
f(x) = x/ 9
C)
f(x) = 9x
D)
f(x) = x + 9 Answer:
C
Solve the problem. 225)
Assume the function f computes the number y in millions of people using the internet in year x. f = {(1996, 1.2), (1998, 4.3), (2000, 9.8) Evaluate f( 2000) and give the domain and range of f
225)
_____ A)
f( 2000) = 1.2; D: {1996, 1998, 2000}, R: {1.2, 4.3, 9.8} B)
f( 2000) = 9.8; D: {1.2, 4.3, 9.8}, R: {1996, 1998, 2000} C)
f( 2000) = 4.3; D: {1.2, 4.3, 9.8}, R: {1996, 1998, 2000} D)
f( 2000) = 9.8; D: {1996, 1998, 2000}, R: {1.2, 4.3, 9.8} Answer:
D
226)
The stretch in a loaded spring varies with the load it supports. If the spring stretches 6.2 cm for every pound of load added, find the distance in centimeters that the spring has stretched when 6 pounds are added.
226)
_____ A)
0.2 cm
B)
37.2 cm
C)
12.2 cm
D)
6 cm Answer:
B
Find the slope of the line that goes through the pair of points. 227)
( 7, -5) and ( 2, 5)
227)
_____ A)
10
B)
5
C)
-2
D)
2 Answer:
C
228)
( -2, -8) and ( 7, 9)
228)
_____ A)
1
B)
1
C)
Undefined
D)
1 Answer:
A
229)
( 6, -2) and ( -3, 7)
229)
_____ A)
Undefined
B)
9
C)
-9
D)
-1 Answer:
D
230)
( -8, -6) and ( -5, 2)
230)
_____ A)
1
B)
Undefined
C)
2
D)
-2 Answer:
C
231)
( 3, -4) and ( 3, 4)
231)
_____ A)
2
B)
Undefined
C)
8
D)
4 Answer:
B
232)
( -1, 6) and ( 9, 6)
232)
_____ A)
0
B)
15
C)
1
D)
5 Answer:
A
State the slope of the graph of f. 233)
f(x) = 2x + 17
233)
_____ A)
-17
B)
0
C)
17
D)
2 Answer:
D
234)
f(x) = x - 7
234)
_____ A)
-7
B)
C)
0
D)
Answer:
D
Solve the problem. 235)
The amount of money, in dollars, raised each year by a band booster club can be estimated by the function f(x) = 198x - 389,484, where x is the year with 1990 ≤ x ≤ 2000. What is the slope of the graph of f?
235)
_____ A)
4536
B)
-198
C)
-389,484
D)
198 Answer:
D
236)
The decline in the value of a stock can be estimated by the function where x is the year with 1990 ≤ x ≤ 2000. What is the slope of the graph of f?
236)
_____ A)
1117.8
B)
83
C)
-0.52
D)
0.52 Answer:
C
State whether the given function is linear and constant, linear but not constant, or nonlinear. 237)
f(x) = -3x + 4
237)
_____ A)
none of these
B)
nonlinear C)
linear, but not constant
D)
linear, constant Answer:
C
238)
f(x) = -2 - 2x + 14
238)
_____ A)
none of these
B)
nonlinear C)
linear, but not constant
D)
linear, constant Answer:
B
239)
f(x) = -3 + 9
239)
_____ A)
none of these
B)
nonlinear C)
linear, constant
D)
linear, but not constant Answer:
B
240)
f(x) = -6 - 7 - 8 + 0.59x - 20
240)
_____ A)
nonlinear
B)
none of these C)
linear, constant
D)
linear, but not constant Answer:
A
241)
f(x) = -0.13x - 1.6
241)
_____ A)
nonlinear
B)
none of these C)
linear, constant
D)
linear, but not constant Answer:
D
242)
f(x) = -7
242)
_____ A)
nonlinear
B)
linear, but not constant C)
none of these
D)
linear, constant Answer:
D
243)
f(x) =
243)
_____ A)
linear, constant
B)
none of these C)
linear, but not constant
D)
nonlinear Answer:
D
Determine if the data in the table are linear or nonlinear. 244)
244)
_____ A)
linear
B)
nonlinear Answer:
A
245)
245)
_____ A)
nonlinear
B)
linear Answer:
B
246)
246)
_____ A)
nonlinear
B)
linear Answer:
A
247)
247)
_____ A)
linear
B)
nonlinear Answer:
A
248)
248)
_____ A)
linear
B)
nonlinear Answer:
B
Represent the function by way of a graph. 249)
At the Big Wave Surfboard Company, the total cost in dollars of manufacturing x surfboards is given by the function Graph f in [0,10,1] by [0,1000,100]
249)
_____ A)
B)
C)
D)
Answer:
C
250)
The total cost in dollars of renting a car for one day is given by the function , where x is the number of miles driven.Graph f in [0,100,10] by [0,100,10]
250)
_____ A)
B)
C)
D)
Answer:
B
251)
The demand, in hundreds of bags of apples, is given by the function , where x is the price per bag, in dollars, of the apples.Graph f in [0,10,1] by [0,50,5]
251)
_____ A)
B)
C)
D)
Answer:
B
252)
The total cost in dollars of a taxi ride is given by the function , where x is the number of miles driven.Graph f in [0,10,1] by [0,10,1].
252)
_____ A)
B)
C)
D)
Answer:
D
253)
The value in dollars of a computer is given by the function , where x is the number of months since the computer is purchased.Graph f in [0,80,10] by [0,3000,500].
253)
_____ A)
B)
C)
D)
Answer:
B
254)
The value in dollars of a rare coin is given by the function , where x is the number of years since the coin was purchased.Graph f in [0,10,1] by [0,1000,100].
254)
_____ A)
B)
C)
D)
Answer:
C
Express the following in interval notation. 255)
x ≥ -3
255)
_____ A)
( -3, ∞)
B)
[ -3, ∞)
C)
(-∞, -3]
D)
(-∞, -3) Answer:
B
256)
x < -41
256)
_____ A)
[ -41, ∞)
B)
(-∞, -41]
C)
( -41, ∞)
D)
(-∞, -41) Answer:
D
257)
4 < x < 8
257)
_____ A)
(-∞, 4] ∪ [ 8, ∞)
B)
( 4, 8)
C)
[ 4, 8]
D)
(-∞, 4) ∪ ( 8, ∞) Answer:
B
258)
-8 ≤ x < 4
258)
_____ A)
( -8, 4]
B)
( -8, 4)
C)
[ -8, 4)
D)
[ -8, 4] Answer:
C
259)
1 ≥ x > -7
259)
_____ A)
(-∞, -7) ∪ [ 1, ∞)
B)
( -7, 1]
C)
[ -7, 1)
D)
(-∞, -7] ∪ ( 1, ∞) Answer:
B
260)
{x|x ≤ 10}
260)
_____ A)
[ 10, ∞)
B)
(-∞, 10)
C)
(-∞, 10]
D)
( 10, ∞) Answer:
C
261)
{x|x > 10}
261)
_____ A)
[ 10, ∞)
B)
(-∞, 10]
C)
(-∞, 10)
D)
( 10, ∞) Answer:
D
262)
{x|-5 < x}
262)
_____ A)
(-∞, -5)
B)
[ -5, ∞)
C)
(-∞, -5]
D)
( -5, ∞) Answer:
D
263)
{x|x < -9 or x > -3}
263)
_____ A)
(-∞, -9) ∪ ( -3, ∞)
B)
(-∞, -9] ∪ [ -3, ∞) C)
( -9, -3)
D)
[ -9, -3] Answer:
A
264)
{x|x < -8 or x ≥ 4}
264)
_____ A)
( -8, 4]
B)
(-∞, -8] ∪ ( 4, ∞)
C)
(-∞, -8) ∪ [ 4, ∞)
D)
[ -8, 4) Answer:
C
265)
265)
_____ A)
(-∞, 4)
B)
( 4, ∞)
C)
[ 4, ∞)
D)
(-∞, 4] Answer:
B
266)
266)
_____ A)
(-∞, -3)
B)
(-∞, -3]
C)
( -3, ∞)
D)
[ -3, ∞) Answer:
B
267)
267)
_____ A)
[ 0, 4]
B)
[ 0, 4)
C)
( 0, 4]
D)
( 0, 4) Answer:
C
268)
268)
_____ A)
( -1, 3]
B)
[ -3, 1)
C)
[ -1, 3)
D)
( -3, 1] Answer:
B
269)
269)
_____ A)
( -2, 2)
B)
[ -2, 2]
C)
[ -2, 2)
D)
( -2, 2] Answer:
D
270)
270)
_____ A)
[ 2, 6)
B)
( -6, -2]
C)
( 2, 6]
D)
[ -6, -2) Answer:
D
271)
271)
_____ A)
[ -2, 2]
B)
(-∞, -2) ∪ ( 2, ∞)
C)
( -2, 2)
D)
(-∞, -2] ∪ [ 2, ∞) Answer:
B
272)
272)
_____ A)
[ 3, 7]
B)
( 3, 7)
C)
(-∞, 3] ∪ [ 7, ∞)
D)
(-∞, 3) ∪ ( 7, ∞) Answer:
C
273)
273)
_____ A)
(-∞, -5] ∪ ( -1, ∞)
B)
(-∞, -5) ∪ ( -1, ∞) C)
[ -5, -1)
D)
(-∞, -5) ∪ [ -1, ∞) Answer:
A
274)
274)
_____ A)
( -6, -2]
B)
(-∞, -6) ∪ ( -2, ∞) C)
(-∞, -6] ∪ ( -2, ∞)
D)
(-∞, -6) ∪ [ -2, ∞) Answer:
D
Use the graph of f to determine the intervals where f is increasing and where f is decreasing. 275)
275)
_____ A)
increasing: (-∞, ∞); decreasing: never
B)
increasing: [ -1, ∞); decreasing (-∞, -1] C)
increasing: (-∞, -1]; decreasing [ -1, ∞)
D)
increasing: (-∞, 0]; decreasing [0, ∞) Answer:
B
276)
276)
_____ A)
increasing: (-∞, ∞); decreasing: never
B)
increasing: [0, ∞); decreasing (-∞, 0] C)
increasing: never; decreasing: (-∞, ∞)
D)
increasing: (-∞, 0]; decreasing [0, ∞) Answer:
B
277)
277)
_____ A)
increasing: never; decreasing: (-∞, ∞)
B)
increasing: (-∞, ∞); decreasing: never C)
increasing: [0, ∞); decreasing (-∞, 0]
D)
increasing: (-∞, 0]; decreasing [0, ∞) Answer:
D
278)
278)
_____ A)
increasing: (-∞, ∞); decreasing: never
B)
increasing: (-∞, -2]; decreasing [ -2, ∞) C)
increasing: [ -2, ∞); decreasing (-∞, -2]
D)
increasing: (-∞, 0]; decreasing [0, ∞) Answer:
B
279)
279)
_____ A)
increasing: (-∞, 0]; decreasing [0, ∞)
B)
increasing: [0, ∞); decreasing (-∞, 0] C)
increasing: (-∞, ∞); decreasing: never
D)
increasing: never; decreasing: (-∞, ∞) Answer:
C
280)
280)
_____ A)
increasing: [0, 3]; decreasing: (-∞, 0] ∪ [3, ∞) B)
increasing: [2, ∞); decreasing: (-∞, 2] C)
increasing: [0, ∞); decreasing: (-∞, 0] D)
increasing: (-∞, 1] ∪ [2, ∞); decreasing: [1, 2] Answer:
A
281)
281)
_____ A)
increasing: [0, ∞); decreasing: (-∞, 0] B)
increasing: [-1, ∞); decreasing: (-∞, -1] C)
increasing: [-1, 1]; decreasing: (-∞, -1] ∪ [1, ∞) D)
increasing: [-1, 0] ∪ [1, ∞); decreasing: (-∞, -1] ∪ [0, 1] Answer:
D
Identify where f is increasing and where f is decreasing. 282)
f(x) = -2
282)
_____ A)
neither
B)
increasing: (-∞, ∞); decreasing: never C)
increasing: [ -2, ∞); decreasing: never
D)
increasing: never; decreasing: [ -2, ∞) Answer:
A
283)
f(x) = 4x + 3
283)
_____ A)
neither
B)
increasing: never; decreasing: (-∞, ∞) C)
increasing: [ 3, ∞); decreasing: (-∞, 3]
D)
increasing: (-∞, ∞); decreasing: never Answer:
D
284)
f(x) = -4x - 3
284)
_____ A)
increasing: (-∞, ∞); decreasing: never
B)
increasing: never; decreasing: (-∞, ∞) C)
neither
D)
increasing: [ -3, ∞); decreasing: (-∞, -3] Answer:
B
285)
f(x) = - 5
285)
_____ A)
increasing: (-∞, 0]; decreasing [0, ∞)
B)
increasing: [0, ∞); decreasing (-∞, 0] C)
increasing: (-∞, ∞); decreasing: never
D)
increasing: [ -5, ∞); decreasing: never Answer:
B
286)
f(x) = 4x -
286)
_____ A)
increasing: (-∞, 2]; decreasing [2, ∞)
B)
increasing: [2, ∞); decreasing (-∞, 2] C)
increasing: [4, ∞); decreasing (-∞, 4]
D)
increasing: (-∞, 4]; decreasing [4, ∞) Answer:
A
287)
f(x) = + 6x
287)
_____ A)
increasing: (-∞, 6]; decreasing [6, ∞)
B)
increasing: [-3, ∞); decreasing (-∞, -3] C)
increasing: [6, ∞); decreasing (-∞, 6]
D)
increasing: (-∞, -3]; decreasing [-3, ∞) Answer:
B
288)
f(x) =
288)
_____ A)
increasing: [ -2, ∞); decreasing: never
B)
increasing: never; decreasing: [-2, ∞) C)
increasing: never; decreasing: [2, ∞)
D)
increasing: [ 2, ∞); decreasing: never Answer:
D
289)
f(x) = -
289)
_____ A)
increasing: never; decreasing: [8, ∞)
B)
increasing: never; decreasing: [-8, ∞) C)
increasing: [ 8, ∞); decreasing: never
D)
increasing: [ -8, ∞); decreasing: never Answer:
B
290)
f(x) =
290)
_____ A)
increasing: [ -4, ∞); decreasing: (-∞, -4]
B)
increasing: [ 4, ∞); decreasing: (-∞, 4] C)
increasing: (-∞, 4]; decreasing: [4, ∞)
D)
increasing: (-∞, -4]; decreasing: [-4, ∞) Answer:
B
291)
f(x) =
291)
_____ A)
increasing: [ 6, ∞); decreasing: (-∞, 6]
B)
increasing: (-∞, -6]; decreasing: [-6, ∞) C)
increasing: (-∞, 6]; decreasing: [6, ∞)
D)
increasing: [ -6, ∞); decreasing: (-∞, -6] Answer:
D
Identify where f is increasing or where f is decreasing, as indicated. Round your answer to two decimal places when appropriate.
292)
f(x) = -3 + 12x; increasing
292)
_____ A)
(-∞, -2]
B)
[ 2, ∞)
C)
[ -2, ∞)
D)
(-∞, 2] Answer:
D
293)
f(x) = -6 + 12x - 4; decreasing
293)
_____ A)
(-∞, -1]
B)
[ 1, ∞)
C)
[ -1, ∞)
D)
(-∞, 1] Answer:
B
294)
f(x) = ; increasing
294)
_____ A)
(-∞, 0.20]
B)
(-∞, ∞)
C)
[-0.20, 0.20]
D)
[ 0.20, ∞) Answer:
D
295)
f(x) = - 7x - 7; decreasing
295)
_____ A)
[-2.65, 2.65]
B)
(-∞, -1.53] C)
[-1.53, 1.53]
D)
(-∞, -1.53] ∪ [ 1.53, ∞) Answer:
C
296)
f(x) = - 9 + 18; decreasing
296)
_____ A)
(-∞, -2.45) ∪ ( -1.73, 1.73) ∪ ( 2.45, ∞)
B)
( -2.12, 0) ∪ ( 2.12, ∞) C)
( -2.45, -1.73) ∪ ( 1.73, 2.45)
D)
(-∞, -2.12) ∪ (0, 2.12) Answer:
D
Use the graph and formula for f(x) to find the average rates of change of f from -4 to -1 and from 1 to 4.
297)
f(x) = 3
297)
_____ A)
0; 0
B)
-3; -3
C)
3; -3
D)
3; 3 Answer:
A
298)
f(x) = 4x - 3
298)
_____ A)
-4; 4
B)
4; 4
C)
-4; -4
D)
3; 3 Answer:
B
299)
f(x) = -3x + 2
299)
_____ A)
-3; -3
B)
3; -3
C)
3; 3
D)
-3; 3 Answer:
A
300)
f(x) = 0.4 - 3
300)
_____ A)
2; -2
B)
2; 2
C)
-2; -2
D)
-2; 2 Answer:
D
301)
y = -0.4 + 3
301)
_____ A)
2; 2
B)
-2; 2
C)
2; -2
D)
-2; -2 Answer:
C
Compute the average rate of change of f from to . Round your answer to two decimal places whenappropriate. Interpret your result graphically.
302)
f(x) = 8x + 1, = -5 and = -2
302)
_____ A)
7; the slope of the line passing through (-5, f(-5)) and (-2, f(-2)) is 7. B)
8; the slope of the line passing through (-5, f(-5)) and (-2, f(-2)) is 8. C)
9; the slope of the line passing through (-5, f(-5)) and (-2, f(-2)) is 9. D)
10; the slope of the line passing through (-5, f(-5)) and (-2, f(-2)) is 10. Answer:
B
303)
f(x) = -5x + 1, = -4 and = -1
303)
_____ A)
-6; the slope of the line passing through (-4, f(-4)) and (-1, f(-1)) is -6. B)
-5; the slope of the line passing through (-4, f(-4)) and (-1, f(-1)) is -5. C)
5; the slope of the line passing through (-4, f(-4)) and (-1, f(-1)) is 5. D)
4; the slope of the line passing through (-4, f(-4)) and (-1, f(-1)) is 4. Answer:
B
304)
f(x) = - 4x, = 2 and = 4
304)
_____ A)
-24; the slope of the line passing through (2, f(2)) and (4, f(4)) is -24. B)
8; the slope of the line passing through (2, f(2)) and (4, f(4)) is 8. C)
-8; the slope of the line passing through (2, f(2)) and (4, f(4)) is -8. D)
24; the slope of the line passing through (2, f(2)) and (4, f(4)) is 24. Answer:
D
305)
f(x) = , = 1 and = 3
305)
_____ A)
0.38; the slope of the line passing through (1, f(1)) and (3, f(3)) is 0.38. B)
-0.38; the slope of the line passing through (1, f(1)) and (3, f(3)) is -0.38. C)
-1; the slope of the line passing through (1, f(1)) and (3, f(3)) is -1. D)
1; the slope of the line passing through (1, f(1)) and (3, f(3)) is 1. Answer:
A
Complete the following for the given f(x).(i) Find f(x + h).(ii) Find the difference quotient of f and simplify.
306)
f(x) = 5
306)
_____ A)
(i) 5(ii) 5
B)
(i) h + 5(ii) h
C)
(i) h + 5(ii) 0
D)
(i) 5(ii) 0
Answer:
D
307)
f(x) = -6x
307)
_____ A)
(i) -6x + 6h(ii) -6
B)
(i) -6x - 6h(ii) 6
C)
(i) -6x + 6h(ii) 6
D)
(i) -6x - 6h(ii) -6
Answer:
D
308)
f(x) = 6x - 10
308)
_____ A)
(i) 6x + 6h - 10(ii) -6
B)
(i) 6x + h - 10(ii) 6
C)
(i) 6x + 6h - 10(ii) 6
D)
(i) 6x + 6h - 10(ii) 10
Answer:
C
309)
f(x) = - 4x
309)
_____ A)
(i) + - 4x - 4h(ii) h - 4
B)
(i) + 2xh + - 4x - 4h(ii) 2xh + h - 4x
C)
(i) + 2xh + - 4x + h(ii) 2x + h + 1
D)
(i) + 2xh + - 4x - 4h(ii) 2x + h - 4
Answer:
D
310)
f(x) = 8x2 + 11x - 9
310)
_____ A)
(i) 8 + 16xh + 8 + 11x + 11h - 9(ii) 16xh + 11h + 8h2
B)
(i) 8 + 8xh + 8 + 11x + 11h - 9(ii) 8x + 6 + 16h
C)
(i) 8 + 16xh + 8 + 11x - 9(ii) 16x + 11
D)
(i) 8 + 16xh + 8 + 11x + 11h - 9(ii) 16x + 8h + 11
Answer:
D
Solve the problem. 311)
The profit (in millions of dollars) for Allied Manufacturing can be approximated by where x is the year 1989 ≤ x ≤ 2009. Approximate the average rate of change over a 7-year period. Round your answer to three decimal places when appropriate.
311)
_____ A)
3.908 million dollars
B)
2.338 million dollars C)
1.838 million dollars
D)
4.348 million dollars Answer:
B
312)
The profit (in millions of dollars) for Allied Manufacturing can be approximated by where x is the year 1989 ≤ x ≤ 2009. Approximate the average rate of change over a 7-year period. Round your answer to three decimal places when appropriate.
312)
_____ A)
-2.023 million dollars
B)
-1.213 million dollars C)
-2.233 million dollars
D)
-7.633 million dollars Answer:
A
313)
The following table gives the outside temperature in degrees Fahrenheit on a winter day in Death Valley, California.
Calculate the average rate of change in temperature between 8:00 am and 11:00 am. Round your answer to two decimal places when appropriate.
313)
_____ A)
4.70°F
B)
3.98°F
C)
2.60°F
D)
3.67°F Answer:
D
314)
The distance D in feet that an object has fallen after t seconds is given by D(t) = 16 . (i) Evaluate D( 2) and D( 5). (ii) Calculate the average rate of change of D from 2 to 5. Interpret the result.
314)
_____ A)
(i) 64, 400 (ii) 112; the object's average speed from 2 to 5 seconds is 112 ft/sec.
B)
(i) 32, 80 (ii) 112; the object's average speed from 2 to 5 seconds is 112 ft/sec.
C)
(i) 32, 80 (ii) 48; the object's average speed from 2 to 5 seconds is 48 ft/sec.
D)
(i) 64, 400 (ii) 48; the object's average speed from 2 to 5 seconds is 48 ft/sec.
Answer:
A
315)
Let the number of gallons G of water drained from a pool after t hours be given by for
(i) Find G(t + h). (ii) Find the difference quotient. Interpret your result.
315)
_____ A)
(i) 3750 - 150t + 150h(ii) -150; the pool is being emptied at a constant rate of 150 gal/hr.
B)
(i) 3750 - 150t + 150h(ii) 150; the pool is being emptied at a constant rate of 150 gal/hr.
C)
(i) 3750 - 150t + h(ii) 1; the pool is being emptied at a constant rate of 1 gal/hr.
D)
(i) 3750 - 150t - 150h(ii) -150; the pool is being emptied at a constant rate of 150 gal/hr.
Answer:
D
1)
B 2)
B 3)
D 4)
A 5)
C 6)
A 7)
A 8)
B 9)
B 10)
B 11)
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D 107)
Answers may vary. A possible answer follows.
108)
Answers may vary. A possible answer follows.
109)
Answers may vary. The following is a possible answer.
110)
Answers may vary. A possible answer follows.
111)
Answers may vary. A possible answer follows.
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D 148)
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D 310)
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A 313)
D 314)
A 315)
D
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