MAC1147 Test-2 Review
Name___________________________________ Date:_________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find functions f and g so that f g = H.
1
1) H(x) =
x-4
A) g(x) =
x ; f(x) =
C) f(x) = x - 4; g(x) =
1)
1
x-4
B) f(x) =
1
; g(x) =
x-4
1
x
D) f(x) =
1
1
; g(x) =
x-4
x
For the given functions f and g, find the requested composite function.
Find (g f)(x).
2) f(x) = 4x2 + 6x + 5, g(x) = 6x - 6;
A) 24x2 + 36x + 36
B) 24x2 + 36x + 24
C) 4x2 + 6x - 1
The function f is one-to-one. Find its inverse.
6
3) f(x) =
x+4
D) 4x2 + 36x + 24
2)
3)
4 + 6x 2
A) f-1 (x) =
x
B) f-1 (x) =
4 + 6x
C) f-1 (x) =
x
-4x + 6
D) f-1 (x) =
x
Indicate whether the function is one-to-one.
4) {(5, 4), (6, 4), (7, 9), (8, 5)}
A) Yes
x
B) No
Graph the function.
5) f(x) = 2 - x - 1
x
4 + 6x
4)
5)
Professor J. Prieto-Valdes 1
A)
B)
C)
D)
Solve the equation.
1 3x + 6
= 9 x- 2
6)
3
A) -
2
5
6)
B)
10
3
C) - 1
D) -
4
5
Solve the problem.
7) The bacteria in a 10-liter container double every 2 minutes. After 57 minutes the container is full.
How long did it take to fill a quarter of the container?
A) 53 min
B) 42.8 min
C) 28.5 min
D) 14.3 min
Professor J. Prieto-Valdes 2
7)
Graph the function.
8) f(x) = -4 - ln x
8)
A)
B)
C)
D)
Change the logarithmic expression to an equivalent expression involving an exponent.
9) log b 81 = 4
A) 814 = b
B) b4 = 81
C) 81b = 4
Graph the function.
Professor J. Prieto-Valdes 3
9)
D) 4 b = 81
10) f(x) =
1
log 3 x
2
10)
A)
B)
C)
D)
Professor J. Prieto-Valdes 4
11) f(x) = 2 - ln(x + 4)
11)
A)
B)
C)
D)
Write as the sum and/or difference of logarithms. Express powers as factors.
11
(7x) 1 + 2x
,
x>4
12) ln
(x - 4)9
A) 7ln x +
2
ln (1 + 2x) - 9ln (x - 4)
11
B) ln 7 + ln x +
1
ln (1 + 2x) - 9ln (x - 4)
11
C) ln 7 + ln x +
1
ln (1 + 2x) - ln 9 - ln (x - 4)
11
D) ln 7 + ln x - 11ln (1 + 2x) - 9ln (x - 4)
Professor J. Prieto-Valdes 5
12)
Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places.
13) log 0.804
13)
7
A) -8.920
B) 8.706
C) -0.112
D) -0.095
Write as the sum and/or difference of logarithms. Express powers as factors.
x4
14) log 2
y6
14)
2
x
log 2
3
y
A) 4 log 2 x - 6 log 2 y
B)
C) 4 log 2 x + 6 log 2 y
D) 6 log 2 y - 4 log 2 x
Express as a single logarithm.
15) log c t + log c s
t
A) log c
s
15)
B) log c ts
C) log c (ts)
D) log c t · log c s
Solve the equation.
1
16) 3 (6 + 3x) =
27
A) {3}
16)
B) {-3}
17) log (5x) = log 4 + log (x - 1)
3
4
A)
B) 4
9
18) log3 x + log3 (x - 24) = 4
A) {-3, 27}
C) {9}
D)
1
9
17)
C) - 4
D) 4
C) {53}
D)
18)
B) {27}
Use a graphing calculator to solve the equation. Round your answer to two decimal places.
19) log3 x + log5 x = 3
A) {1.92}
B) {0.85}
C) {7.09}
D) {12.82}
Solve the equation.
20) log 5 (x + 4) = 2
A) {29}
19)
20)
B) {36}
C) {21}
D) {28}
Solve the problem.
21) The population of a particular country was 26 million in 1981; in 1988, it was 34 million. The
exponential growth function A =26ekt describes the population of this country t years after 1981.
Use the fact that 7 years after 1981 the population increased by 8 million to find k to three decimal
places.
A) 0.038
B) 0.048
C) 0.297
D) 0.969
Professor J. Prieto-Valdes 6
21)
Find the amount that results from the investment.
22) $12,000 invested at 12% compounded quarterly after a period of 8 years
A) $29,711.56
B) $30,000.96
C) $18,900.99
23) $1,000 invested at 11% compounded semiannually after a period of 8 years
A) $1355.26
B) $2355.26
C) $2304.54
Solve the system of equations.
24)
x+y+ z= 8
x - y + 3z = 6
5x + y + z = 28
A) x = 1, y = 5, z = 2; (1, 5, 2)
C) x = 5, y = 2, z = 1; (5, 2, 1)
D) $30,900.99
D) $2232.48
22)
23)
24)
B) x = 1, y = 2, z = 5; (1, 2, 5)
D) inconsistent
25)
25)
7x + 7y + z = 1
x + 8y + 8z = 8
9x + y + 9z = 9
A) x = 0, y = 0, z = 1; (0, 0, 1)
C) x = -1, y = 1, z = 1; (-1, 1, 1)
B) x = 1, y = -1, z = 1; (1, -1, 1)
D) x = 0, y = 1, z = 0; (0, 1, 0)
Write the augmented matrix for the system.
-2x +4z = 18
26)
2y +7z = 41
9x +3y +9z = 63
A)
-2 0 9 18
0 2 3 41
4 7 9 63
B)
26)
-2 0 4
027
939
C)
-2 0 4 18
0 2 7 41
9 3 9 63
D)
Perform the row operation(s) on the given augmented matrix.
27) R 3 = 4r1 + r3
-7 -5 -1 -10
6 -2 9
5
28 -6 6 18
-7 -5 -1
A) 6 -2 9
0 -26 10
-7 -5 -1
C) 6 -2 9
0 16 10
-10
5
-22
-10
5
-22
-2 4 0 18
2 7 0 41
9 3 9 63
27)
-7
6
0
-7
D) 6
0
B)
-5 -1
-2 9
16 2
-5 -1
-2 9
-26 2
-10
5
-22
-10
5
-22
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.
x - y + 3z = -1
28) 5x
28)
+ z=1
x + 4y + z = 17
A) x = 0, y = 4, z = 1; (0, 4, 1)
B) x = 1, y = 0, z = 4; (1, 0, 4)
C) x = 1, y = 4, z = 0; (1, 4, 0)
D) x = 0, y = 1, z = 4; (0, 1, 4)
Professor J. Prieto-Valdes 7
Solve for x.
29)
5 -3 1
-2 -2 x = 28
8
2 -1
A) 2
29)
B) -1
C) 1
D) 0
Solve the system of equations using Cramer's Rule if it is applicable. If Cramer's Rule is not applicable, say so.
2x - 3y = 6
30) 6x - 9y = 24
30)
15
5 15
5
,y=- ;
,A) x =
B) x = 6, y = 24; (6, 24)
4
2 4
2
C) not applicable
Find the value of the determinant.
31)
1 2 3
2 1 5
1 2 3
A) 0
D) x = 3, y = 4; (3, 4)
31)
B) 1
C) 50
D) -20
Solve the system of equations using substitution.
32)
xy = 40
x2 + y2 = 89
32)
A) x = 8, y = -8; x = -8, y = -5; x = 5, y = 8; x = -5, y = -8
or (8, -8), (-8, -5), (5, 8), (-5, -8)
B) x = 8, y = 5; x = 5, y = 8; x = 8, y = -5; x = 5, y = -8
or (8, 5), (5, 8), (8, -5), (5, -8)
C) x = -8, y = -5; x = -5, y = -8; x = -8, y = 5; x = -5, y = 8
or (-8, -5), (-5, -8), (-8, 5), (-5, 8)
D) x = 8, y = 5; x = -8, y = -5; x = 8, y = -5; x = -8, y = 5
or (8, 5), (-8, -5), (8, -5), (-8, 5)
33)
x2 + y2 = 13
x + y = 5
A) x = -3, y = -2; x = -2, y = -3
or (-3, -2), (-2, -3)
C) x = 3, y = -2; x = 2, y = -3
or (3, -2), (2, -3)
33)
B) x = -3, y = 2; x = -2, y = 3
or (-3, 2), (-2, 3)
D) x = 3, y = 2; x = 2, y = 3
or (3, 2), (2, 3)
Professor J. Prieto-Valdes 8
Find the vertex, focus, and directrix of the parabola with the given equation.
34) (y - 2)2 = -8(x + 1)
A) vertex: (-1, 2)
focus: (1, 2)
directrix: x = -3
C) vertex: (2, -1)
focus: (0, -1)
directrix: x = 4
34)
B) vertex: (-1, 2)
focus: (-3, 2)
directrix: x = 1
D) vertex: (1, -2)
focus: (-1, -2)
directrix: x = 3
Find an equation of the parabola described.
35) Focus at (3, 0); directrix the line x = -3
A) y2 = -12x
B) y2 = 3x
C) x2 = 12y
D) y2 = 12x
Find an equation for the ellipse described.
36) Center at (0, 0); focus at (0, 2); vertex at (0, -8)
x2 y2
x2 y2
+
=1
+
=1
A)
B)
4
64
4
60
x2 y2
+
=1
C)
60 64
x2 y2
+
=1
D)
64 60
Professor J. Prieto-Valdes 9
35)
36)
Graph the hyperbola.
(x + 1)2 (y - 2)2
=1
37)
9
16
37)
A)
B)
C)
D)
Professor J. Prieto-Valdes 10
Graph the ellipse and locate the foci.
x2 y2
+
=1
38)
9
16
A) foci at (0,
7) and (0, - 7)
C) foci at (4, 0) and (-4, 0)
38)
B) foci at (5, 0) and (-5, 0)
D) foci at ( 7, 0) and (- 7, 0)
Professor J. Prieto-Valdes 11
Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
x2
y2
=1
39)
144 100
A) center at (0, 0)
transverse axis is y-axis
vertices at (0, -12) and (0, 12)
foci at (- 2 61, 0) and (2 61, 0)
5
5
asymptotes of y = - and y =
6
6
B) center at (0, 0)
transverse axis is x-axis
vertices at (-12, 0) and (12, 0)
foci at (-10, 0) and (10, 0)
5
5
asymptotes of y = - and y =
6
6
C) center at (0, 0)
transverse axis is x-axis
vertices at (-12, 0) and (12, 0)
foci at (- 2 61, 0) and (2 61, 0)
5
5
asymptotes of y = - and y =
6
6
D) center at (0, 0)
transverse axis is x-axis
vertices at (-10, 0) and (10, 0)
foci at (- 2 61, 0) and (2 61, 0)
5
5
asymptotes of y = - and y =
6
6
Find the asymptotes of the hyperbola.
(x - 2)2 (y + 1)2
=1
40)
25
9
39)
40)
A) y - 2 =
3
3
(x + 1) and y - 2 = - (x + 1)
5
5
B) y + 1 =
C) y + 1 =
3
3
(x - 2) and y + 1 = - (x - 2)
5
5
D) y =
5
5
(x - 2) and y + 1 = - (x - 2)
3
3
3
3
(x - 2) and y = - (x - 2)
5
5
Professor J. Prieto-Valdes 12
Answer Key
Testname: MAC1147 TES-2 REVIEW
1)
2)
3)
4)
5)
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7)
8)
9)
10)
11)
12)
13)
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15)
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17)
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26)
27)
28)
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31)
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40)
B
B
D
B
B
A
A
A
B
C
A
B
C
A
B
B
C
B
C
C
A
D
B
C
A
C
D
A
D
C
A
A
D
B
D
C
D
A
C
C
Professor J. Prieto-Valdes 13