Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Draw the interval on a number line.
1) (-3, 6]
1)
A)
B)
C)
D)
2) [-4, 2)
2)
A)
B)
C)
D)
3) [5, ∞)
3)
A)
B)
C)
D)
1
4) [-3, 2π)
5) (-
4)
A)
B)
C)
D)
2, 8)
5)
A)
B)
C)
D)
6) Use intervals to describe the real numbers satisfying the inequality, x < 9, x ≥ -2.
A) [-9, 2)
B) [-2, 9)
C) (-2, 9)
D) (-2, 9]
E) none of these
6)
7) Use intervals to describe the real numbers satisfying the inequality, x ≥
A) (-∞, 7]
B) ( 7, ∞)
C) (-∞, 7)
D) [ 7, ∞)
E) none of these
7)
Use intervals to describe the real numbers satisfying the inequality.
8) x ≤ 3
A) (-∞, 3)
B) (-∞, 3]
C) [-∞, 3]
7.
8)
D) [3, ∞)
9) -9 < x < -4
A) [-9, -4)
9)
B) (-9, -4)
C) [-9, -4]
D) (-9, -4]
10) 2 ≤ x ≤ 10
A) [2, 10]
B) [2, 10)
C) (2, 10)
D) (2, 10]
10)
2
Evaluate the function.
11) f(x) = x 2 + 2x - 2; Find f(0).
A) 0
B) 2
C) -2
D) 4
12) f(x) = 5x2 - 3x + 4; Find f(1).
A) 12
B) 2
C) 6
D) -2
13) f(x) =
A)
11)
12)
3x ; Find f(-3).
6x + 1
13)
9
17
B)
3
7
C)
14) f(x) = 3x2 + 2x + 4; Find f(t - 1).
A) 3t2 - 4t + 5
B) -4t2 + 3t + 5
1
2
D) - 9
14)
C) 3t2 + 14t + 9
D) 3t2 - 4t + 9
Evaluate the function for the given value.
x-5
if x ≠ - 1
15) f(x) = 2x + 2
; f -1
12
A) 12
16) f(x) =
15)
if x = - 1
B) - 12
x-5
2x + 1
if x ≠ -
1
2
12
if x = -
1 ; f(5)
2
A) 12
C) - 6
D) 0
16)
B) 0
C) 60
D)
1
11
17) If f(x) = 1 + x, find f(9).
A) 3
B) 3
C) 10
D) 2
E) none of these
18) If f(x) =
A)
4
5
17)
2x , find f(-2).
x2 + 1
B) - 4
5
18)
C) -2
D)
3
4
3
E) 0
19) For f(x) = -x2 + 3x + 1 compute f(x + 1).
A) -x2 + 3x + 5
19)
B) -x2 + x + 3
C) -x2 + 3x + 3
D) -x2 + 5x + 5
E) none of these
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
20) Let f(x) =
x+4
. Find f(1) = a, f(-1) = b, f(2) = c.
2
x + 4x + 4
20)
Enter your answer exactly as :
f(1)=a, f(-1)=b, f(2)=c
using reduced fractions or integers for a,b, and c.
21) Let g(x) =
1
25 - x2
. Find g(-4).
21)
Enter your answer exactly in the form:
g(-4)=a/b
where a and b are integers, and a/b is in lowest terms.
2
22) If h(t) = t , find h(a + 2) .
t-6
22)
Enter your answer exactly in the form:
h(a + 2) = P(a)
Q(a)
Where P and Q are polynomials in standard form.
23) Is the point 1 , 2 on the graph of the function f(x) = (x + 1)2 - x ?
2
2
23)
Enter your answer as just the word yes or the word no.
24) Compute f(-2), f(0), and f(3) where f(x) =
x2
for -5 ≤ x ≤ -1
1
x-2
for -1 < x ≤ 2
12 - x
24)
for 2 < x
Enter your answer exactly in the form:
a,b,c
where a < b < c and are either fractions of the form d/e in lowest terms or integers.
25) If f(3) = 5 + a and (3, -1) is on the graph of f, find a.
Enter your answer as just an integer, no variables.
4
25)
Use the following graph to solve the problem.
26)
26)
Are all of the following true? Enter your answer exactly as just the word true or the
word false.
(a) f(3) = 2
(b) f(5) = 0
(c) f(-2) is negative
(d) f(6) is negative
(e) f(2) is greater than f(4)
(f) f(x) = 0 for x=0,5
(g) f(x) ≤ 0 on (-∞, 0] ∪ [5, ∞)
27) Consider the curve f(x) in the accompanying sketch.
Find f(2). Enter your answer as just an integer.
5
27)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the graph to evaluate the function f(x) at the indicated value of x.
28) Find f(0.5).
A) 0
C) -1
28)
B) -0.5
D) None of these are correct.
29) Find f(0.5).
29)
A) -1
C) 1
B) 0
D) None of these are correct.
6
30) If f(x) =
(I)
4x
, which of the following are true?
8(x + 2)(-x - 1)
30)
-1 is the domain
1
f
=- 1
2
15
(II)
(III)
f(0) = - 1
16
(IV)
f is not defined at x = -2 and x = -1
A) II and IV
B) I and II
C) I and IV
D) II and III
E) none of these
31) Which of the following pairs of points lie on the line -x + 3y = 12?
A) (1, 3) and (0, 2)
B) (12, 0) and (0, 4)
C) (0, 12) and (2, 6)
D) (-12, 0) and (0, 4)
32) Describe the domain of the function f(x) =
31)
1
.
(x - 1)2(x - 3)
32)
A) x ≠ 1, 3
B) x = 1, 3
C) x ≠ -1, -3, and f(2) = 1
D) x ≠ 1 , and f(0) = 1
3
E) none of these
33) Describe the domain of the function f(x) =
1
.
1-x
33)
A) x ≥ 1
B) x ≤ 1
C) x ≥ 0
D) x < 1
E) none of these
State the domain of the given function.
34) f(x) = x
x-5
A) x = 5
35) f(x) =
34)
B) x > 5
C) x ≠ 5
D) All x
8
7x - 6
A) x ≠
7
6
35)
B) x ≠
6
7
C) x >
7
6
7
D) All x
36) f(x) = x + 7
A) x ≥ 7
B) x > -7
C) x ≥ -7
D) x ≠ -7
37) f(x) = -x - 8
A) x ≥ 8
B) x ≥ -8
C) x ≤ -8
D) x ≤ 8
38) f(x) =
36)
37)
3x
2
x -1
A) All x
38)
B) x ≥ 1
C) x ≠ 1
D) x ≠ -1, 1
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
39) Describe the domain of f(x) = (x + 1)(x + 2) x - 3 .
(x2 + 1)(x2 + 5)
39)
Enter your answer in standard interval notation.
No variables.
40) Describe the domain of g(x) =
2-x .
(x + 1)(x - 3)
40)
Enter your answer in standard interval notation.
No variables.
41) Describe the domain of f(x) = x + x + 1 + x - 1 +
Enter your answer in standard interval notation.
No variables.
42) Describe the domain of the function g(x) =
x+5.
x+3
x+3 -
x - 4.
41)
42)
Enter your answer in standard interval notation.
No variables.
43) Describe the domain of the function f(z) =
5z
.
(z + 3) z - 2
Enter your answer in standard interval notation.
No variables.
8
43)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
44) Decide which curve is the graph of a function.
A)
44)
B)
C)
D) none of these
45) Decide which of the curves below are graphs of functions?
(I)
(II)
(III)
A) I only
B) I and III only
C) I and II only
D) all of these
E) none of these
9
45)
Decide whether the graph represents a function.
46)
46)
A) Function
B) Not a function
47)
47)
A) Function
B) Not a function
48)
48)
A) Function
B) Not a function
10
49)
49)
A) Function
B) Not a function
50)
50)
A) Function
B) Not a function
51)
51)
A) Function
B) Not a function
Solve the problem.
52) If the average cost per unit C(x) to produce x units of plywood is given by C(x) = 600 , what is
x + 20
the unit cost for 20 units?
A) $30.00
B) $1.50
C) $15.00
11
D) $10.00
52)
53) The graph shows the relationship between the area A of a rectangle and the length L, if the
width is fixed. Find the area if the length is 16 cm.
A) 182 cm2
B) 252 cm2
C) 224 cm2
D) 196 cm2
54) The height of a baseball that is thrown from ground level with an initial velocity of 67 feet per
second can be modeled by h(t) = -16t2 + 67t. Find the height of the ball after 2.1 seconds.
A) 73.5 ft
B) 211.26 ft
C) 137.56 ft
54)
D) 70.14 ft
55) The price Luke charges for shipping items from his home business is based on the total order
amount. For orders up to $300 he charges 5% of the total amount. For orders over $300 he
charges 3% of the total plus $15.00. If x is the amount of the sale (in dollars), express the
shipping charge as a function of x.
for 0 ≤ x ≤ 300
A) f(x) = 5x
B) f(x) = 0.05x for 0 ≤ x ≤ 300
3x + 15.00 for 300 < x
15.00 for 300 < x
0.05x
for
0
≤
x
≤
300
C) f(x) =
D) f(x) = 0.03x + 15.00 for 0 ≤ x ≤ 300
0.03x + 15.00 for 300 < x
0.05x
for 300 < x
12
53)
55)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
56) Is this the graph of the function y = - 1 x + 2?
3
56)
Enter your answer as just the word yes or the word no.
-2
-6 ≤ x ≤ 1 ?
x-3
1<x≤6
Enter your answer as just the word yes or the word no.
57) Is the following the graph of f(x) =
13
57)
58) Is this the graph of the function f(x) =
2x + 6
3x
30 - 3 x
7
7
for 0 ≤ x < 2
for 2 ≤ x ≤ 3
for x > 3
?
58)
Enter your answer as just the word yes or the word no.
59) Is this the graph of the following function: f(x) =
1 ?
x+5
Enter your answer as just the word yes or the word no.
14
59)
60) Is this the graph of the following function: f (x) = 2x + x ?
Enter just the word yes or the word no.
60)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Graph the equation.
61) y = 2x - 1
61)
A)
B)
15
C)
D)
62) x = 4
62)
A)
B)
16
C)
D)
63) y + 4 = 0
63)
A)
B)
17
C)
64) y = -
D)
1
x+5
3
64)
A)
B)
18
C)
D)
65) 3y + 5x = 12
65)
A)
B)
19
C)
D)
66) 3x + y = -1
66)
A)
B)
20
C)
D)
67) 6x - 30y = 0
67)
A)
B)
21
C)
Graph the function.
3,
68) f(x) =
x+1,
D)
for x ≤ 2,
for x > 2
68)
A)
B)
22
C)
69) f(x) =
D)
x - 5, for x < 1,
2,
for x ≥ 1
69)
A)
B)
23
C)
70) f(x) =
D)
-5 - x, for x < 1,
-3,
for x ≥ 1
70)
A)
B)
24
C)
71) f(x) =
D)
2 - x, for x ≤ 2,
1 - 3x, for x > 2
71)
A)
B)
25
C)
72) f(x) =
D)
4x + 2,
x,
3x - 1,
for x < -2,
for -2 ≤ x ≤ 3,
for x > 3
72)
A)
B)
26
C)
D)
73) Determine the y-intercept of the graph of the following function: y = 3x + 8.
A) (8, 0)
8
B) 0, 3
73)
C) - 8 , 0
3
D) (0, 8)
E) none of these
74) Determine the intercepts of the graph of f(x) = -4x - 3 .
4
74)
3
A) -3 , 0 and 0,
16
4
B)
3 , 0 and 0, -3
4
16
-3
C) -3 , 0 and 0,
4
16
D) 3,0 and 0,
-3
4
E) -3,0 and 0,
-3
4
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
75) Determine the intercepts of the following function: f(x) = 5 - 2x.
Enter your answer exactly as two ordered pairs, with the x-intercept first.
76) Determine the y- intercept of the following function: f(x) = 3.
Enter your answer as just an ordered pair.
27
75)
76)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine the intercepts on the graph of the equation.
77) f(x) = 7x + 5
A) 5 , 0 ; (0, 5)
B) - 5 , 0 ; (0, 5)
7
7
77)
C) (5, 0); 0, -
5
7
D) -
7
, 0 ; (0, 7)
5
78) f(x) = 2x
A) (1, 0); (0, -2)
B) (0, 0); (0, 2)
C) (0, 0)
D) (2, 0); (0, 0)
78)
79) y = x + 2
A) (2, 0); (0, -2)
B) (0, 0)
C) (-2, 0); (0, 2)
D) (2, 0); (0, 2)
79)
80) y = -7x - 1
A) 1 , 0 ; (0, 1)
7
C) (-1, 0); 0,
80)
B) 1 , 0 ; (0, -7)
7
1
7
D) - 1 , 0 ; (0, -1)
7
81) The quadratic function y = -9x - 8x2 + 5 has the form y = ax2 + bx + c.
Identify a, b, and c in the order a, b, c.
A) -8, -9, 5
B) 9, 8, 5
C) -9, -8, 5
D) 5, -8, -9
E) none of these
81)
2
82) The quadratic function, y = 8x + 7x - 2 , has the form y = ax2 + bx + c. Identify a, b, and c.
4
82)
A) 8, 7, -2
B) 2, 7 , - 1
4
2
C) 8, 7, 2
D) -2, - 7 , 1
4 2
E) none of these
The given quadratic function has the form y = ax2 + bx + c. Identify a, b, and c.
83) y = 3 - 5x2
A) a = 3
b = -5
c=0
B) a = -5
b=3
c=0
C) a = -5
b=0
c=3
28
83)
D) a = 5
b=0
c=3
84) y = 1 x2 - 6πx +
8
A) a = 1
8
b = -6π
c= 6
6
84)
B) a = 1
8
C) a = 8
b = -6π
c=6
b = 6π
c= 6
D) a = 1
8
b=6
c= 6
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
85) Evaluate f(x) = 3 - x when x = -6.
Enter your answer exactly in the form: f(-6) = a
where a is an integer.
85)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Evaluate the function at the given value of x.
86) f(x) = x , x = 18-4
A) f(18-4) = 72
87) f(x) = x490, x = -1
A) f(-1) = 490
86)
B) f(18-4) = 18-4
C) f(18-4) = 184
D) f(18-4) = 22
B) f(-1) = -490
C) f(-1) = 1
D) f(-1) = -1
87)
Solve the problem.
88) In a certain city, the cost of a taxi ride is computed as follows: There is a fixed charge of $2.50 as
soon as you get in the taxi, to which a charge of $1.95 per mile is added. Express the cost of an
x-mile taxi ride as a function of the number of miles driven.
A) C(x) = 2.50x + 1.95
B) C(x) = 4.45x
C) C(x) = 1.95x + 2.50
D) C(x) = 2.95x
88)
89) A moving firm charges a flat fee of $45 plus $40 per hour. Express the cost of a move as a
function of the hours it takes to complete the move.
A) C(x) = 45x - 40
B) C(x) = 45x + 40
C) C(x) = 40x + 45
D) C(x) = 40x - 45
89)
90) A cab company charges a base rate of $2.00 plus 20 cents per minute. Express the cost of a cab
ride as a function of the number of minutes the ride takes.
A) C(x) = 2.00x - 0.20
B) C(x) = 2.00x + 0.20
C) C(x) = 0.20x + 2.00
D) C(x) = 0.20x - 2.00
90)
91) An electrician charges a fee of $60 plus $45 per hour. Express the cost of the electrician's services
as a function of the amount of time he spends on the job.
A) C(x) = 45x - 60
B) C(x) = 60x + 45
C) C(x) = 45x + 60
D) C(x) = 60x - 45
91)
92) A cable TV company charges $23 per month for the basic service plus $6 for each movie channel.
Express the cost of a monthly cable bill as a function of additional movie channels.
A) C(x) = 23x + 6
B) C(x) = 6x + 23
C) C(x) = 23x - 6
D) C(x) = 6x - 23
92)
29
93) A store is discounting all regularly priced items by 30%. (i) Find a function f that computes the
sale price of an item having a regular price of x. (ii) If an item normally costs $116.58, what is its
sale price?
A) f(x) = 0.3x; $34.97
B) f(x) = x - 30; $86.58
C) f(x) = x - 0.3x; $81.61
D) f(x) = x - 0.3; $116.28
93)
94) A store is discounting all regularly priced items by 50%. (i) Find a function f that computes the
sale price of an item having a regular price of x. (ii) Find the regular price of an item that costs
$84.48 on sale.
A) f(x) = 0.5 + x; $83.98
B) f(x) = x - 0.5; $84.98
C) f(x) = 0.5x; $168.96
D) f(x) = x - 0.5x; $168.96
94)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Let f (x) = x2 - x + 2, and g(x) = 4x + 5. Calculate the following function(s):
95) f(x) + g(x)
Enter your answer exactly as a polynomial in standard form.
Do not label the polynomial.
96) f(x)g(x)
Enter your answer exactly as a polynomial in standard form.
Do not label the polynomial.
Let f (x) = x6 + 1, g(x) = x3 + 1. Calculate the following function(s) and express in simplest terms:
97) f(x) + g(x)
Enter your answer exactly as a polynomial in standard form.
Do not label the polynomial.
98) f(x) - g(x)
Enter your answer exactly as a polynomial in standard form.
Do not label the polynomial.
99)
f(x) for x ≠ -1
g(x)
95)
96)
97)
98)
99)
Enter your answer as exactly P(x) where P and Q are polynomials in standard form.
Q(x)
Do not label your answer.
100) f(x)g(x)
Enter your answer exactly as a polynomial in standard form.
Do not label the polynomial.
Let f (x) =
100)
x and g(x) = 2 . Calculate the following function(s) and express in simplest terms:
x-1
x+1
101) f(x) + g(x) for x ≠ ±1
101)
Enter your answer exactly as P(x) where P and Q are polynomials in standard form.
Q(x)
Do not label your answer.
30
102) f(x) - g(x) where x ≠ ±1
102)
Enter your answer exactly as P(x) where P and Q are polynomials in standard form.
Q(x)
Do not label your answer.
103) f(x)g(x) where x ≠ ± 1
103)
Enter your answer exactly as P(x) where P and Q are polynomials in standard form.
Q(x)
Do not label your answer.
104)
f(x) where x ≠ ± 1
g(x)
104)
Enter your answer as exactly P(x) where P and Q are polynomials in standard form.
Q(x)
Do not label your answer.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the given functions to find the requested function.
105) f(x) = 4x + 9, g(x) = 5x2
105)
Find (fg)(x).
A) 20x + 45
B) 20x2 + 45x
C) 20x3+ 45x2
D) 5x2 + 4x + 9
106) f(x) = 2x + 8, g(x) = 3x2
Find (f + g)(x).
A) 6x3 + 24x
107) f(x) = 2x + 8, g(x) = 4x2
Find (g - f)(x).
A) 4x2 - 2x - 8
106)
B)
2x + 8
3x2
C) 2x + 8 - 3x2
D) 3x2 + 2x + 8
107)
B) 2x + 8 - 4x2
C) -2x3 + 4x2
D) 4x2 - 2x + 8
108) f(x) = 6x + 5, g(x) = 3x2
Find (g/f)(x).
A)
6x + 5
3x2
108)
B) 3x2 + 6x + 5
C)
3x2
6x + 5
D) 18x2 + 15x
109) f(x) = 5x2 - 9x, g(x) =x2 - 5x - 36
Find f/g.
A)
5x - 9
-5
B)
109)
5-x
36
C)
31
5x
x+1
D)
5x2 - 9x
x2 - 5x - 36
Express the following as a rational function.
110) f(x) = 4x - 3 ; g(x) = 2x
3x - 8
3x - 8
110)
Find f - g.
A) (f - g)(x) = 6x + 3
3x - 8
B) (f - g)(x) = -2x + 3
3x - 8
C) (f - g)(x) = -2x - 3
3x - 8
D) (f - g)(x) = 2x - 3
3x - 8
111) f(x) =
x ; g(x) = 3x + 3
x+3
x-3
111)
Find f(x + 3)
g(x + 3)
A)
C)
x2 + 3x
B)
3x2 + 30x + 72
3x2 + 3x
D)
x2 + 30x + 72
x+3
2
3x + 9x + 24
x2 + 3x
3x2 + 30x + 24
112) f(x) = x - 6
x+6
Find f
A)
112)
1
t
1 - 6t
1 + 6t
B)
1 + 6t
1 - 6t
C)
6t + 1
6t - 1
D)
6t - 1
6t + 1
Find f(x + h) - f(x) and simplify.
h
113) f(x) = x2 - 5x
A) h - 5
114) Let f(x) =
113)
B) 2xh + h - 5x
C) 2x + h + 1
1 , and g(x) = 1 x≠ -1, -2. Calculate g(f(x)).
x+1
x+2
A)
x
3x + 2
B)
x+1
x+2
C)
x+1 ,x≠- 3
2x + 3
2
D)
x+1
3x + 2
E) none of these
32
D) 2x + h - 5
114)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Let f (x) = x2 - x + 2, and g(x) = 4x + 5. Calculate the following function(s):
115) f(g(x))
Enter your answer exactly as a polynomial in standard form.
Do not label the polynomial.
115)
Let f (x) = x6 + 1, g(x) = x3 + 1. Calculate the following function(s) and express in simplest terms:
116) f(g(x))
Do not simplify your answer at all.
116)
Let f (x) =
x and g(x) = 2 . Calculate the following function(s) and express in simplest terms:
x-1
x+1
117) f(g(x)) where x ≠ ± 1
117)
Enter you answer as exactly P(x) where P and Q are polynomials in standard form.
Q(x)
Do not label your answer.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
118) If f(x) = 5x + 14 and g(x) = 2x - 1, find f(g(x)).
A) 10x + 13
B) 10x + 9
C) 10x + 27
D) 10x + 19
119) If f(x) = -5x + 7 and g(x) = 3x + 9, find g(f(x)).
A) -15x + 52
B) 15x + 30
C) -15x + 30
D) -15x - 12
118)
119)
120) If f(x) = 4x 2 + 6x + 3 and g(x) = 6x - 5, find g(f(x)).
A) 24x2 + 36x + 13
C) 4x2 + 36x + 13
120)
B) 4x2 + 6x - 2
D) 24x2 + 36x + 23
121) A stone is thrown into a pond. A circular ripple is spreading over the pond in such a way that
the radius is increasing at the rate of 5.7 feet per second, modeled by the function r(t) = 5.7t. The
area of a circular ripple is given by the function A(x) = πx2, where x is the radius of the circle.
Express the area of the ripple as a (composite) function of the number of seconds that have
passed since the stone entered the pond.
A) A(r(t)) = 32.49πt2
B) A(r(t)) = 32.49π2t
C) A(r(t)) = 11.4πt2
D) A(r(t)) = 5.7πt2
33
121)
122) The table below shows a conversion table for women's shoe sizes in three different countries.
The function g(x) = 4x + 5 converts from Country A sizes to Country B sizes, and the function
f(x) = 0.25x converts from Country B sizes to Country C sizes. Determine the function
h(x) = f(g(x)) and give its interpretation.
Country A 4
5
6
7
Country B 21
25
29
33
Country C 5.25 6.25 7.25 8.25
A) h(x) = x + 5; converts from Country A sizes to Country B sizes, then back to Country A
sizes
B) h(x) = 4x + 1.25; converts from Country A sizes to Country C sizes
C) h(x) = x + 1.25; converts from Country A sizes to Country C sizes
D) h(x) = x - 1.25; converts from Country C sizes to Country A sizes
122)
123) Compute the number, (0.000008)1/3.
A) 0.024
B) 0.2
C) 0.0027
D) 0.02
E) none of these
123)
124) Compute the number, 162.25 .
A) 268
B) 64
C) 36
D) 512
E) none of these
124)
125) Compute the number, (3125) 0.6 .
A) 1875
B) 628
C) 125
D) 2521
E) none of these
125)
126) Compute the number, (0.0001)-1.25 .
A) 10,000
B) 12,500
C) 125,000
D) 100,000
E) none of these
126)
127) Evaluate f(32) for f(x) = x7/5.
A) 64
B) 128
C) 8
D) 256
E) none of these
127)
34
128) Evaluate f(19) for f(x) = x0.
A) 10
B) 19
C) 1
D) 0
E) none of these
128)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Compute the number(s).
129) 84/3 Enter your answer as an integer.
129)
130) 32859630 Enter your answer as an integer.
130)
131) 2162/3 Enter your answer as an integer.
131)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Evaluate the expression. Write your answer without exponents.
132) 5-3
1
1
A)
B) -125
C)
125
-125
132)
D) 125
1
133) -4
8
133)
A) 4096
B) 512
C) 32
D) 32,768
3-3
134) -2
7
A)
135)
134)
343
81
B)
27
49
C)
49
27
D)
81
343
1
-5-2
A) 25
135)
B) 5
C) -5
D) -25
C) 2
1
D)
2
136) (-2)-1
A) - 1
2
136)
B) -2
137) (-5)-2
137)
1
25
A) -25
B)
A) 1
B) -1
C)
1
-25
D) 25
138) 20
138)
C) 0
35
D) 2
139) (-4)0
A) -4
140)
139)
B) -1
C) 0
D) 1
7 -2
8
A)
140)
8
49
B)
64
49
C)
1
49
D)
49
64
Evaluate the expression.
141) 271/3
141)
A) 3
B) 81
C) 9
D) 243
142) -2431/5
A) 81
B) -27
C) 243
D) -3
143)
142)
49 1/2
81
A)
7
10
144) 84/3
A) 64
143)
B)
6
10
C)
7
9
D)
6
9
144)
B) 16
C) 128
D) 32
1
B)
25
C) - 1
25
1
D)
5
145) 125-2/3
A) -25
146)
145)
125 -2/3
64
A)
16
125
146)
B)
16
25
25
16
C) -
D)
25
16
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Use the laws of exponents to compute the number.
3/4
147) (81/3)2
Enter your answer as ab/c where a, b, c are integers.
147)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
148)
123
43
A) 9
148)
B) 3
C) 64
36
D) 27
149) (216 ∙ 64)1/3
A) 72
149)
B) 10
C) 280
150) Use the laws of exponents to simplify the algebraic expression (
A) (x + 5)1/2
D) 24
1/4
x + 5)3
.
150)
B) (x + 5)3/8
C) (x + 5)3/2
D) (x + 5)3/4
E) none of these
151) Use the laws of exponents to simplify the algebraic expression (x + 3)4/3 ∙ (x - 2)-1/3 2.
(x + 3)8/3
A)
(x- 2)2/3
151)
(x + 3)8/3
(x - 2)3
B)
C) (x2 +x - 6)2
1
D)
2
(x + x - 6)8/3
E) none of these
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Use the laws of exponents to simplify the algebraic expression. Your answer should not involve parentheses or
negative exponents.
x7
Enter your answer as xay b where a and b are integers.
152)
152)
9
-3
y x
153) (9x)-3/2 Enter your answer as: a xc/d where a, b, c, and d are integers
b
154)
155)
156)
x
3
1/3
1
8x3
x2 ∙
5
Enter your answer as: a xc/d where a, b, c, and d are integers.
b
x4 Enter your answer as: xa/b where a, b are integers.
1
Enter your answer as: xay b where a, b are integers.
-5
-2
x y
37
153)
154)
155)
156)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the expression. Write your answer without negative exponents. Whenever an exponent is negative or zero,
assume that the base is not zero.
157) (x-6)3
157)
A) -6x18
B)
1
x18
C) -6x3
D) -x18
158) (x2)-9
158)
1
B)
x18
A) -9x2
C) -9x18
D) - x18
159) (x-4)-3
A)
160)
159)
1
x12
B) -x7
1
x7
D) x12
x12
x6
160)
A) x6
161)
C)
B) x18
C)
1
x6
D) x8
-5x -3
y4
A)
161)
y 12
B)
125x3
5y 12
x3
12
C) - y
125x3
12
D) - 5y
x3
Calculate the following function. Take x > 0.
5
1
162) Let f(x) = x and g(x) =
x8
Find g(x)[f(x)]5
1
A)
x7
163) Let f(x) =
3
Find g(f(x))
1
A)
4/3
x
x and g(x) =
162)
B) x7
C) x9/8
D)
1
x8
1
x4
163)
B) x3/4
C) x4/3
38
D)
1
3/4
x
164) The expression may be factored as shown. Find the missing factor.
17x4/5 + x-1/5 = x-1/5(
)
164)
A) 17x + 1
B) 17x + x4/5
C) 17x6/5 + x4/5
D) 17x6/5 + x
E) none of these
165) The expression may be factored as shown. Find the missing factor.
2x
+
y
y
=
x
A)
x2 + 2y 2
2xy
B)
x2 + y 2
2xy
C)
x2 + 2y 2
2xy
D)
2x2 + y 2
2xy
2xy(
165)
)
E) none of these
166) Calculate the compound amount from the given data:
principal = $10,000, compounded annually, 18 years, annual rate = 6%
A) $20,200.00
B) $26,927.73
C) $28,543.39
167) Calculate the compound amount from the given data:
principal = $14,000, compounded semiannually, 9 years, annual rate = 4%
A) $16,731.30
B) $19,926.37
C) $19,040.00
168) Calculate the compound amount from the given data:
principal = $600, compounded quarterly, 2 years, annual rate = 16%
A) $648.96
B) $807.36
C) $821.14
169) Calculate the compound amount from the given data:
principal = $1770, compounded annually 9 years, annual rate = 6%
A) $2619.60
B) $2821.11
C) $2725.80
166)
D) $20,800.00
167)
D) $19,995.45
168)
D) $792.00
169)
D) $2990.38
Solve the problem.
170) Universal Bank lends $3,800,000 for 1
1
years at 8% compounded quarterly to Shining Shores
2
Development Company to fund the building of a condominium complex. Find the value at the
1
end of the 1 years.
2
A) $4,265,001.90
B) $4,279,417.20
C) $6,030,122.42
39
D) $4,256,000.00
170)
171) Lexi can invest $7370 for 3 years at 10% compounded quarterly. Find the value at the end of the
3 years.
A) $9581.00
B) $231,302,171.61
C) $98,094,700.00
D) $9911.83
171)
172) Suppose that a $200 investment earns interest compounded semiannually. Express the value of
the investment after 2 years as a polynomial in the annual rate of interest r.
25
25
A) A =
(16 + 32r + 24r2 + 8r3 + r4)
B) A =
(8 + 16r + 12r2 + 4r3 + r4)
2
2
172)
C) A =
25
(16r4 + 32r3 + 24r2 + 8r + 1)
2
D) A = 200(16 + 32r + 24r2 + 8r3 + r4)
40
Answer Key
Testname: UNTITLED1
1) D
2) B
3) B
4) A
5) D
6) B
7) D
8) B
9) B
10) A
11) C
12) C
13) A
14) A
15) A
16) B
17) D
18) B
19) B
20) f(1) = 5 , f(-1) = 3, f(2) = 3
9
8
21) g(-4) = 1
3
2
22) h(a + 2) = a + 4a + 4
a-4
23) yes
24) - 1 , 3,4
2
25) -6
26) true
27) 2
28) A
29) C
30) A
31) D
32) A
33) D
34) C
35) B
36) C
37) C
38) D
39) [3, ∞)
40) (-∞, -1) ∪ (-1, 3) ∪ (3, ∞)
41) [4, ∞)
42) [-5, -3) ∪ (-3, ∞)
43) (2, ∞)
41
Answer Key
Testname: UNTITLED1
44) B
45) B
46) A
47) A
48) B
49) B
50) A
51) A
52) C
53) C
54) D
55) C
56) yes
57) yes
58) no
59) yes
60) yes
61) B
62) D
63) C
64) B
65) D
66) D
67) A
68) C
69) B
70) B
71) A
72) D
73) D
74) C
75) 5 , 0 , (0, 5)
2
76) (0, 3)
77) B
78) C
79) C
80) D
81) A
82) B
83) C
84) A
85) f(-6) = 3
86) B
87) C
88) C
89) C
42
Answer Key
Testname: UNTITLED1
90) C
91) C
92) B
93) C
94) D
95) x2 + 3x + 7
96) 4x3 + x2 + 3x + 10
97) x6 + x3 + 2
98) x6 - x3
(x6 + 1)
99)
(x3 + 1)
100) x9 + x6 + x3 + 1
x2 + 3x - 2
101)
x2 - 1
102)
x2 - x + 2
x2 - 1
103)
2x
2
x -1
104)
x2 + x
2x - 2
105) C
106) D
107) A
108) C
109) D
110) D
111) A
112) A
113) D
114) C
115) 16x2 + 36x + 22
116) (x3 + 1)6 + 1
117)
2
-x+1
118) B
119) C
120) A
121) A
122) C
123) D
124) D
125) C
126) D
43
Answer Key
Testname: UNTITLED1
127) B
128) C
129) 16
130) 1
131) 36
132) A
133) A
134) C
135) D
136) A
137) B
138) A
139) D
140) B
141) A
142) D
143) C
144) B
145) B
146) B
147) 23/2
148) D
149) D
150) B
151) A
x10
152)
y9
153)
1
27x3/2
154)
1
2x1/2
155) x22/15
156) x5y 2
157) B
158) B
159) D
160) A
161) C
162) A
163) A
164) A
165) E
166) C
167) D
168) C
169) D
44
Answer Key
Testname: UNTITLED1
170) B
171) D
172) A
45