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Practice test for Test 4- 1314-Fall 2010
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine whether or not the function is one -to-one.
1)
1) f(x) = 9 - x2
A) Yes
B) No
2) f(x) = (-4x - 2) 2
2)
A) No
B) Yes
Decide whether or not the functions are inverses of each other.
1
3) f(x) = 4x + 16, g(x) = x - 4
4
A) Yes
4) f(x) = 3)
B) No
1 + x
1
, g(x) = x
x - 1
4)
A) No
B) Yes
5)
5)
10
y
9
8
7
6
5
4
3
2
1
1
2
3
4
5
6
7
8
9 10 x
A) Yes
B) No
1
6)
6)
10
y
9
8
7
6
5
4
3
2
1
1
2
3
4
5
6
7
8
9 10 x
A) Yes
B) No
If f is one-to-one, find an equation for its inverse.
7) f(x) = -5x + 1
7)
1
A) f-1 (x) = - x + 1
5
1
1
B) f-1 (x) = - x + 5
5
1
C) f-1 (x) = - x - 1
5
1
1
D) f-1 (x) = - x - 5
5
Find the domain and range of the inverse of the given function.
8) f(x) = x - 5
8)
A) Domain and range: all real numbers
B) Domain: [0, ∞); range: [5, ∞)
C) Domain: [5, ∞); range: [0, ∞)
D) Domain: all real numbers; range: [5, ∞)
9) f(x) = 1
x + 2
9)
A) Domain: (-∞, 0) ∪ (0, ∞); range (-∞, -2) ∪ (-2, ∞)
B) Domain all real numbers; range (-∞, -2) ∪ (-2, ∞)
C) Domain and range are all real numbers
D) Domain: (-∞, -2) ∪ (-2, ∞) ; range (-∞, 0) ∪ (0, ∞)
Graph the exponential function using transformations where appropriate.
2
10) f(x) = 3 x - 2
10)
y
10
5
-10
-5
5
10
x
-5
-10
A)
B)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C)
5
10
x
5
10
x
D)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
Solve the equation.
11) 2 (5 - 3x) = A) {3}
1
16
11)
B) {8}
C)
3
1
8
D) {-3}
12) 1 x
= 49
7
A)
1
2
12)
B) - 13) 16x - 4 = 644x
8
A) - 3
1
2
C) {2}
D) {-2}
4
C) - 5
1
D) - 5
C) 0
8
D)
3
13)
4
B) - 3
14) ( 7 ) x + 4 = 49x
14)
4
B)
3
A) 4
Find the present value of the future value.
15) $4000, invested for 9 years at 10% compounded monthly
A) $1722.35
B) $1632.35
15)
C) $9801.79
D) $9711.79
Solve the problem.
16) Find the required annual interest rate, to the nearest tenth of a percent, for $1762 to grow to
$28,541 if interest is compounded annually for 32 years.
A) 6.8%
B) 9.1%
C) 18.2%
D) 4.5%
17) An element decays at the rate of S(t) = se-0.076t, where s is the initial amount in grams and t is
the time in years since this initial amount was present. If you have a 41-gram piece of this
element, how many grams will you have 2 years from now? Round your answer to the nearest
tenth of a gram.
A) 19.0
B) 0.9
C) 47.7
1
= 2
-3 8
19) 4 3/2 = 8
log 8
2 = 4
A)
log 4
3
17)
D) 35.2
Write in logarithmic form.
1
18) 2 -3 = 8
A) log
16)
18)
1
B) log -3 = 2
8
C) log
1/8
2 = -3
D) log
1
= -3
2 8
19)
3
B) log 4 = 3
2
3
C) log 8 = 4
2
Write an equivalent expression in exponential form.
1
20) log = -2
2 4
1 2
= 2
B) 2 1/4 = 2
A)
4
3
D) log 4 = 8
2
20)
C) 2 -2 = 4
1
4
D) 2 2 = 1
4
21) log
64 = 6
4
A) 4 3 = 64
21)
B) 4 64 = 3
C) 3 4 = 64
D) 643 = 4
Solve the equation.
22) x = 4 log4 11
22)
B) 11
A) 4
D) -11
C) 44
23) log6 6 10 = x
A) { 5}
23)
B) {5}
C) {30}
D) {60}
3
24) x = log3 81
A)
3
4
24)
B) - 4
3
C) 12
D)
4
3
Write the expression as a sum, difference, or product of logarithms. Assume that all variables represent positive real
numbers.
25) loga(4x2 y)
25)
A) loga 4 + 2loga x + loga y
B) (loga 4 )(loga x) (loga y)
C) loga 4 + (loga x)2 + loga y
D) loga (4 + x2 + y)
26) log5 (12x + 9y)
26)
A) log5 108xy
B) log5 12x + log5 9y
C) log5 (12x + 9y)
D) (log5 12x) (log5 9y)
27) log19 4 m
n
27)
1
A) log19 4 + log19 m - log19 n
2
B) log19 4 + log19 m - log19 n
1
C) log19 4 · log19 m ÷ log19 n
2
1
D) log19 n - log19 4 - log19 m
2
Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all
variables represent positive real numbers.
28) (loga m - loga n) + 4 loga k
28)
A) loga mk4
n
B) loga C) loga m
k4 n
D) loga (m + k4 - n)
5
4mk
n
7
4
logn 5y + logn (25y2 )
2
7
29)
29)
A) logn (125y39/40)
B) logn (5 65/14 y65/14)
C) logn (5 39/20 y 63/40 )
D) logn (125y9/10)
30) 6 log6 (6x - 1) + 4 log6 (2x - 7)
Given log
30)
A) log6 ((6x - 1)6 + (2x - 7)4 )
B) log6 (6x - 1)6 (2x - 7)4
C) 24 log6 (6x - 1)(2x - 7)
D) log6 10
2 = 0.3010 and log
31) log
10
(6x - 1)6
(2x - 7)4
3 = 0.4771, find the logarithm without using a calculator.
27
10 4
A) 1.8572
31)
B) 0.0512
C) 0.2549
D) 0.8293
Use the change of base rule to find the logarithm to four decimal places.
32) log
7.0
240
A) 0.3551
32)
B) 2.3802
C) 2.8165
D) 34.2857
Solve the problem.
33) Let u = ln a and v = ln b. Write the following expression in terms of u and v without using the
function ln.
5
ln ( ab7 )
u 7
7
7
u 7
u
B) - v
C) u + v
D) + v
A) - 7v
5 5
5
5
5 5
5
33)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
34) Given f(x) = ln x, evaluate the following.
(a) f(e3 )
34)
(b) f(eln 3 )
(c) f(e 3 ln 3 )
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
35)
35) log8 x = log 8 x
A) {8}
B) {1, 8}
C) {0, 8}
6
D) {0, 1}
36) log3 (log3 x) = 1
A) {6}
36)
B) {3}
C) {9}
D) {27}
Solve the equation and express the solution in exact form.
37) log9 (x - 7) + log9 (x - 7) = 1
A) 10
37)
B)
50
38) log(x + 10) = 1 + log(4x - 3)
13
40
B)
, 1
A)
3
39
C) - 50, 50
D) -10, 10
C) 1
40
D)
39
38)
Solve for the indicated variable.
39) I - Io = (I1 -Io)10-kt , for t
39)
I - Io
1
B) t = - log k
I1 - Io
1
A) t = - log (I - I1 )
k
C) t = - I - Io
k(I1 - Io)
1
I
D) t = - log k
I1
Solve the problem.
40) In the formula N = Iekt , N is the number of items in terms of an initial population I at a given time
t and k is a growth constant equal to the percent of growth per unit time. How long will it take for
the population of a certain country to triple if its annual growth rate is 2.8%? Round to the nearest
year.
A) 17 years
B) 39 years
C) 107 years
D) 1 year
41) The decay of 481 mg of an isotope is given by A(t) = 481e-0.012t, where t is time in years. Find the
amount left after 46 years.
A) 139 mg
B) 274 mg
C) 277 mg
7
40)
D) 475 mg
41)
Answer Key
Testname: PTEST3‐1314‐FALL2010
1) B
2) A
3) A
4) B
5) B
6) A
7) B
8) B
9) A
10) D
11) A
12) D
13) C
14) B
15) B
16) B
17) D
18) D
19) C
20) C
21) A
22) B
23) B
24) D
25) A
26) C
27) A
28) A
29) B
30) B
31) D
32) C
33) D
34) (a) 3 (b) ln 3 (c) 3 ln 3 or ln 27
35) B
36) D
37) A
38) D
39) B
40) B
41) C
8