Houston Community College
Math 1314: College Algebra
Final Exam Review
This review consists of questions that are representative of the questions that would be on the final examination. This
review provides a good place to start studying for the examination. The answers are provided on the last page. Turn in
this review along with all work to receive up to five bonus points on your final examination.
1) (3.1) Give the x–interecepts (if they exist) and the y–intercept of f(x) = –x2 + 9x – 20
a) No x–intercepts; y–intercept (0, 4)
b) x–intercepts (–4, 0), (–5, 0); y–intercept (0, –20)
c) x–intercepts (4, 0) and (5, 0); y–intercept (0, –20)
d) x–intercepts (4, 0), (5, 0); y–intercept (0, 4)
2) (4.2) Solve the equation:
a) –3
b)
3) (4.5) Solve the equation: log(3 + x) – log(x – 3) = log 5
4) (2.7) Find (f – g)(–2) if f(x) = –5x2 + 1 and g(x) = x + 3
5) (5.5) Give all solutions to the system:
c)
d) 3
a)
b) 4.5
a) –20 b) –14
c) 2.5
d) –4.5
c) –24 d) 21
a) {(4, 3), (–4, 3), (4, –3), (–4, –3)}
b) {(4, 3), (4, –3)}
c) {(4, 3), (3, 4), (–4, –3), (–3, –4)}
d) {(–4, –3), (–3, –4)}
6) (4.1) Determine whether or not the function is one–to–one.
a) Yes
b) No
7) (4.3) Find the value of
a) 6
b)
c) 18
d) –3
8) (2.6) Select the equation that describes the graph shown.
a) y = (x – 2)2 + 3 b) y = (x – 2)2
c) y = (x + 2)2
d) y = x2 – 2
9) (2.1) Find the distance between the points, and find the midpoint of the line segment joining them. (9, 1) and (–1, 9)
a) 2; (10, –8)
b)
; (4, 5)
c) 2; (8, 10)
d)
; (5, 4)
Math 1314: College Algebra
Final Review
HCC
10) (1.6) Use factoring to solve the equation: 8x3 – 125 = 0
a)
,
b) –
,
c)
11) (2.7) Find the composite function,
a) –15x + 32
d)
,
, when f(x) = –5x + 7 and g(x) = 3x + 5
b) –15x – 16
c) 15x + 26
12) (3.5) Find the vertical asymptotes of
.
a) None
d) –15x + 26
b) x = 8
c) x = 2, x = –2 d) x = –8
13) (1.7) Solve the inequality and give the answer in interval notation.
a)
b)
c)
d)
14) (3.5) Give the equation of the vertical asymptote(s) of
a) x = 0, x = 4
b) x = 0, x = –4
c) y = 0
d) x = 1
15) (5.1) Find the length of a rectangular lot with a perimeter of 100 meters if the length is 4 meters more than the width.
(P = 2L + 2W)
a) 27 m
b) 50 m
c) 23 m
d) 54 m
16) (4.1) Determine whether f and g are inverse functions. f(x) =
,
g(x) = x a) Yes
b) No
17) (3.4) How many real zeros does this graph have?
a) 1
b) 3
c) 2
d) 4
18) (4.3) Convert to exponential form:
a)
b) 464 = 3
c)
19) (3.5) Find the domain (D) and the range (R).
a) D = (–∞, ∞); R = (–∞, 0) or (0, ∞)
c) D = (–∞, 11) or (11, ∞); R = (–∞, 0) or (0, ∞)
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b) D = (–∞,11) or (11, ∞); R = (–∞,∞)
d) D = (–∞,∞); R = (–∞,∞)
d)
Math 1314: College Algebra
Final Review
HCC
20) (3.1) Find the equation of the parabola.
a) y = (x – 1)2 + 3 b) y = (x + 1)2 – 3
c) y = (x – 1)2 – 3
d) y = (x + 1)2 + 3
21) (2.7) Find g(x + h) – g(x) when g(x) = x2 – 5
a) 2xh + h2 + 5
b) 2xh + h2 – 5
c) 2x
d) h2 – 5
22) (3.1) Paul sells helium balloons. He has found that his profit is represented by the function P(x) = –x2 + 48x + 23, with
P being profits and x the number of helium balloons. How many helium balloons must he sell to earn the most profit?
a) 48
b) 24
c) 23
23) (2.7) Find (f + g)(–4) if f(x) = x – 5 and g(x) = x – 6
d) 25
a) –9
b) –19
c) 3
d) –7
24) (4.3) Choose the expression that is equivalent to
a) log4 7 – log4 13
b) log8 7 + log8 13
c) log8 7 – log8 13
25) (3.5) Find the equation of the horizontal asymptote of
. a) y = 1
26) (2.5) Find the value of f(0) for
a) 4
d) log8 13 – log8 7
b) y = –2
b) –7 c) –3
c) y = 2
d) None
d) 8
27) (3.2) Use the remainder theorem and synthetic division to find f(–4) when f(x) = 4x4 + 4x3 + 2x2 – 8x + 44.
a) 1616
b) –52
c) 876
28) (4.3) Solve the equation. logx 1024 = 5
a) 205 b) 1029
c) 4
d) 1172
d) 5120
29) (2.2) Find the domain (D) and the range (R) for the function.
a) D = (–∞, 1) or (1, ∞); R = (–∞, 2) or (2, ∞)
b) D = (–∞,∞); R = (–∞,∞)
c) D = (–∞, 2) or (2, ∞); R = (–∞, 1) or (1, ∞)
d) D = (–∞, –1) or (–1, ∞); R = (–∞, –2) or (–2, ∞)
30) (2.7) Find (f + g)(x) when f(x) = –2 – 6x and g(x) = –9x + 6
a) –15x + 4
b) 3x + 8
c) –9x + 2
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d) –7x
Math 1314: College Algebra
Final Review
HCC
31) (3.4) Graph the polynomial function. f(x) = 2x(x + 2)(x + 1)
a)
b)
c)
d)
c)
d)
32) (1.6) Use factoring to solve the equation. 8x3 – 27 = 0
a)
b)
33) (3.3) Apply the Rational Zeros Theorem to determine all possible rational zeros for the polynomial,
P(x) = 3x3 + 31x2 + 31x + 27.
a)
1,
3,
6,
9,
c)
1,
3,
9,
27
27
b)
1,
1/3,
1/9,
d)
1,
1/3,
3,
34) (1.8) Solve the equation. | 4f – 8 | – 2 = –8 a)
b) φ
1/27,
9,
3
27
c)
d)
35) (3.2) Use synthetic division to find the quotient.
a) 5x + 3
b) x + 5
c) –3x – 5
d) 3x + 5
36) (3.3) Find all zeros and their multiplicities. f(x) = (7x – 2)3(x2 + 16)4
a) Multiplicity 3: 2/7
Multiplicity 4:
4i
b) Multiplicity 3: 2/7
Multiplicity 4:
c) Multiplicity 3: 4/7
4
Multiplicity 4:
4i
d) Multiplicity 3: –2/7
Multiplicity 4:
37) (2.3) Which of the following choices describes a linear function whose graph has a slope of 2?
a) f(x) = –10x + 2
b) y = 2x + 9
c) x = 2
d) 2x – 4y = 9
38) (1.6) Solve the equation. (t + 3)2/3 + 6(t + 3)1/3 + 5 = 0
a) –4, 128
b) –128, –4
c) –5, –1
39) (5.3) Find the determinant of the matrix:
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a) 3
4 of 8
d)
b) 71 c) –45 d) –3
4i
Math 1314: College Algebra
Final Review
HCC
40) (4.1) Find the equation of the inverse of 6x – y = 3
a) f –1(x) =
b) f –1(x) =
c) f –1(x) =
d) f (x) =
41) (2.3) Find the slope of the line that passes through the points (8, –6) and (–13, –14).
a)
b) 4
c)
d)
42) (3.3) Find a polynomial function of lowest degree with only real coefficients and having the zeros 2, –14 and 6 + 9i.
a) f(x) = x4 – 8x3 – 18x2 + 870x – 3276
b) f(x) = x4 – 8x3 + 18x2 – 870x + 3276
c) f(x) = x4 – 55x2 + 1740x – 3276
d) f(x) = x4 – 435x2 + 1740x – 3276
43) (1.7) Solve the inequality and graph the solution set. x2 – 2x < 3
a) (–∞, –3] or [1, ∞)
b) [–3, 1]
c) [–1, 3]
d) (–3, 1)
44) (3.3) Completely factor f(x) = 2x3 – 4x2 – 2x + 4 into linear factors given that 1 is a zero of f(x).
a) 2(x – 1)(x – 2)(x + 1)
b) (x – 1)(x + 2)(2x – 4)
45) (1.4) Solve the equation: 3k2 – 12k + 2 = 0
a)
c) (x – 1)(x + 2)(2x – 2)
b)
d) (x + 1)(x + 2)(2x – 2)
c)
d)
46) (1.5) The length of a rectangular frame is 6 cm more than the width. The area inside the frame is 72 square cm. Find
the width of the frame.
a) 8 cm
b) 6 cm
c) 12 cm
d) 18 cm
47) (3.3) Find all rational zeros and factor f(x) = x3 – 4x2 – 4x + 16.
a) 3, 5, –2; f(x) = (x – 3)(x – 5)(x + 2)
b) –3, –5, 2; f(x) = (x + 3)(x + 5)(x – 2)
c) –2, –4, 2; f(x) = (x – 2)(x + 4)(x + 2)
d) 2, 4, –2; f(x) = (x – 2)(x – 4)(x + 2)
48) (1.7) Solve and graph the inequality. Give answers in interval notation.
a) (–1, ∞)
b) (–∞, –1)
x – 9 < –10
c) [–1, ∞)
49) (4.1) Decide whether or not the functions are inverses of each other. f(x) = 4x – 2,
a) Yes
b) No
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d) (–∞, –1]
Math 1314: College Algebra
Final Review
HCC
50) (3.1) Find the domain and range of the function. f(x) = (x + 1)2 – 5
a) Domain: (–5, ∞); range: (–∞,∞)
b) Domain: (–∞,∞); range: [–5, ∞)
c) Domain: (–1, ∞); range: (–∞,∞)
d) Domain: (–∞,∞); range: (–1, ∞)
51) (3.5) Graph the function: f(x) =
a)
b)
c)
d)
y = (x – 3)2
52) (2.6) Given the equation, find the matching description.
a) Vertex (3, 0); opens upward
b) Vertex (0, 3); opens upward
c) Vertex (3, 0); opens downward
d) Vertex (0, 0); opens downward
53) (5.3) Find the determinant of the matrix.
54) (5.3) Solve for x.
=4
a) –7
a) {–1}
b) {1}
b) 1
c) 8
c) {2}
d) 7
d) {–2}
55) (4.3) Choose the equivalent statement: 7 logm q – 5 logm x2
a)
b)
c)
d)
56) (3.3) Use the factor theorem to determine whether or not the second polynomial is a factor of the first.
8x3 + 21x2 – 10x + 3; x + 3
a) No
b) Yes
57) (5.1) Solve the system.
a)
58) (5.1) Solve the system.
a) (–2, 2)
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b) (–1, 4)
b) (–9, 9)
c) (0, –1)
c) (–1, 1)
d)
d) (1, 3)
Math 1314: College Algebra
Final Review
HCC
59) (1.7) Write the inequality in interval notation. 9 > x > –5
a) [–5, 9]
b) (–5, 9]
c) (–5, 9)
d) [–5, 9)
60) (3.2) Use synthetic division to decide if the given number is a zero of the polynomial. 2; f(x) = 8x3 + x2 + 6x + 3
a) Yes
b) No
61) (4.1) If f is one–to–one, find the equation of its inverse.
a) f –1(x) = x3 + 2
b) f –1(x) = (x – 2)3
c) f –1(x) =
62) (4.3) Evaluate the logarithm.
a) 4
63) (4.2) Solve the equation.
a)
d) f –1(x) = x3 – 2
b)
c)
d) –4
b)
c)
d)
64) (1.5) A boy is flying a kite. The vertical distance of the kite from the ground is 21 feet less than its horizontal distance
from the person flying it. The length of the string is 6 feet more than the horizontal distance. Find the horizontal
distance.
a) 27 feet
b) 30 feet
c) 45 feet
d) 60 feet
65) (1.5) A boat is being pulled into a dock with a rope attached to the boat at water level. When the boat is 8 feet from the
dock, the length of the rope from the boat to the dock is 2 feet shorter than twice the height of the dock above the
water. Find the height of the dock.
a) 6 feet b) 8 feet
c) 10 feet
d) 12 feet
66) (1.6) Solve the equation.
a) {–3, –2}
b) {–3}
c) {–2} d) ∅
67) (1.6) Solve the equation. (x – 1)4 – 8(x – 1)2 + 15 = 0
a) {3, 5}
b)
c) {–3, –5}
d)
68) (1.7) Solve the inequality. Give answers in interval notation. v2 + 8v + 15 > 0
a) [–5, –3]
b) [–3, ∞)
c) (–∞, –5] ∪ [–3, ∞)
69) (2.2) Find the domain (D) and range (R) for f(x) =
a) D = [–9, ∞); R = [0, ∞)
b) D = (–∞,∞); R = [–9, ∞)
c) D = (–∞,∞); R = (–∞,∞)
d) D = [0, ∞); R = (–∞,∞)
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d) (–∞, –5]
Math 1314: College Algebra
Final Review
HCC
70) (2.1) Give the equation for the circle with center at (–3, 0) and radius = 2.
a) (x + 3)2 + y2 = 4
b) x2 + (y + 3)2 = 2
c) x2 + (y – 3)2 = 2
d) (x – 3)2 + y2 = 4
71) (3.3) Find all other zeros of P(x) = x3 – 8x2 + 17x – 30, given that 6 is one zero of P(x).
a)
,
b) 1 + 2i, 1 – 2i
c) –1 + 2i, –1 – 2i
d)
c)
d)
,
72) (3.5) Sketch the graph of the rational function.
a)
b)
73) (2.1) Find the center and the radius of the circle. x2 + y2 – 12x + 10y + 57 = 0
a) (–6, 5), r = 4
b) Not a circle
c) (–5, 6), r = 2
d) (6, –5), r = 2
74) (3.4) Use the intermediate value theorem to show that the polynomial has a real zero between the given values of a
and b.
f(x) = 4x5 – 3x3 + 8x2 + 6; a = –2, b = –1
a) f(a) = 66 and f(b) = –13
b) f(a) = –66 and f(b) = 13
c) f(a) = –65 and f(b) = 14
d) f(a) = 66 and f(b) = 13
75) (4.3) Write the expression as a single logarithm with a coefficient of 1. Assume that all variables represent positive
real numbers.
3 log5 (3x + 4) + 6 log5 (9x + 8)
a)
b) log5 [(3x + 4)3(9x + 8)6]
c) 18 log5[(3x + 4)(9x + 8)]
d) log5[(3x + 4)3 + (9x + 8)6]
1 C
2 A
3 B
4 A
5 A
6 B
7 D
8 D
9 B
10 A
11 D
12 A
13 C
14 B
15 A
16 B
17 B
18 C
19 C
20 D
21 A
22 B
23 B
24 C
25 A
26 B
27 C
28 C
29 A
30 A
31 A
32 D
33 D
34 B
35 D
36 A
37 B
38 B
39 A
40 B
41 C
42 C
43 C
44 A
45 A
46 B
47 D
48 B
49 B
50 B
51 C
52 A
53 A
54 A
55 B
56 A
57 B
58 A
59 D
60 B
61 D
62 C
63 C
64 C
65 A
66 A
67 B
68 C
69 A
70 A
71 B
72 D
73 D
74 B
75 B
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