Math 102 College Algebra - Exam 2 - Fall 2014
Printed Name__________________________________
Section ___________
All questions are multiple choice. Choose the best answer and mark this answer on your exam and on the answer sheet
provided. You will receive four points for each correct response. You may write directly on this exam and you may use
scratch paper if you find you do not have enough space to work.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the vertical line test to determine whether y is a function of x.
1)
1)
y
10
5
-10
-5
5
10
x
-5
-10
A) No
B) Yes
Find the domain and range.
2) y = 9 + x
A) D = (-∞, ∞); R = (-∞, ∞)
C) D = (-∞, ∞); R = [-9, ∞)
2)
B) D = [0, ∞); R = (-∞, ∞)
D) D = [-9, ∞); R = [0, ∞)
Evaluate and simplify.
3) Find f(k - 1) when f(x) = 3x2 + 3x + 2.
A) 3k2 + 9k + 8
B) 3k2 - 3k + 8
3)
C) 3k2 - 3k + 2
1
D) -3k2 + 3k + 2
Solve the problem.
4) Each year, Amanda's salary increased from the previous year. By January 1986, Amanda's annual
salary had increased to $46,200, and by January 1990 it had increased to $124,200. What is the
average rate of change of her salary between January 1986 and January 1990?
A) $5460 per year
B) $19,500 per year
C) $21,550 per year
D) $12,314 per year
Determine the intervals on which the function is increasing, decreasing, and constant.
5)
4)
5)
y
5
4
3
2
1
-5
-4
-3
-2
-1
1
2
3
4
5
x
-1
-2
-3
-4
-5
A) Increasing on (-1, 0) and (3, 5); Decreasing on (0, 3); Constant on (-5, -3)
B) Increasing on (-2, 0) and (3, 4); Decreasing on (-5, -2) and (1, 3)
C) Increasing on (-2, 0) and (3, 5); Decreasing on (1, 3); Constant on (-5, -2)
D) Increasing on (1, 3); Decreasing on (-2, 0) and (3, 5); Constant on (2, 5)
Find the domain and range.
6) f(x) = 25 - x2
6)
A) D = (-∞, -5] ∪ [5, ∞) , R = (-∞, ∞)
C) D = [-5, 5] , R = [0, ∞)
B) D = [ -5, 5] , R = [0, 5]
D) D = (-∞, ∞) , R = [0, ∞)
2
Write the equation of the graph after the indicated transformation(s).
7) The graph of y = x2 is translated 8 units to the left and 9 units downward.
A) y = (x - 9)2 + 8
B) y = (x - 8)2 - 9
C) y = (x + 8)2 - 9
7)
D) y = (x + 9)2 - 8
Find the domain and range.
8) y = x - 4 - 6
8)
A) D = (-∞, ∞), R = ( -∞, -6]
B) D = (-∞, ∞), R = [0, ∞)
C) D = (-∞, ∞), R = (-∞, ∞)
D) D = (-∞, ∞), R = [- 6, ∞)
Evaluate.
9) Find (f/g)(-2) given f(x) = 3x - 5 and g(x) = 5x2 + 14x + 4.
3
11
A) B) 5
C)
4
4
9)
5
D) 4
Find the requested function value.
10) Find (g ∘ f)(-3) when f(x) = -9x - 4 and g(x) = -7x2 + 7x + 4.
A) -1840
B) -3538
C) -40
3
10)
D) 716
Find the requested composition of functions.
11) Given f(x) = x + 10 and g(x) = 8x - 14, find (f ∘ g)(x).
A) 2 2x - 1
B) 8 x + 10 - 14
C) 8 x - 4
11)
D) 2 2x + 1
Perform the indicated operations and write the answer in the form a + bi, where a and b are real numbers.
12) (9 + 6i)(9 + 8i)
A) 129 - 18i
B) 33 + 126i
C) 48i2 + 126i + 81
D) 33 - 126i
Evaluate the indicated power of i.
13) i-27
A) -i
12)
13)
B) -1
Find the product of the complex number and its conjugate.
14) -7 - 2i
A) 45
B) 56
C) i
D) 1
C) 54
D) 53
14)
4
Use synthetic division to find the remainder when:
15) (4x3 + 6x2 + 5x + 18) is divided by (x + 3).
A) -279
15)
B) -51
C) -165
D) -21
Factor the polynomial completely, given that the binomial is a factor.
16) x + 9, x3 + 27x2 + 242x + 720
16)
B) (x + 9)(x2 + 18x + 80)
A) (x + 9)(x + 8)(x + 10)
C) (x + 9)(x2 - 18x + 80)
D) (x + 9)(x2 + 80)
Use the rational zero theorem to find all possible rational zeros for the polynomial function.
17) P(x) = -2x4 + 4x3 + 3x2 + 18
A) ±1, ±2, ±
C) ±1, ±
1
1
1
1
1
,± ,± ,± ,±
2
3
6
9
18
B) ±1, ±
1
, ±2, ±3, ±6, ±9, ±18
2
1
3
9
, ±2, ±3, ± , ±6, ±9, ± , ±18
2
2
2
D) ±1, ±2, ±3, ±6, ±9, ±18
Find all of the real and imaginary zeros for the polynomial function, provided 3i is a root.
18) f(x) = x3 + 2x2 + 9x + 18
A) - 2, - 2, 3i
17)
B) -2, - 3, - 3
C) -2, -3i, 3i
5
D) -2, 18i, 9i
18)
Find all of the real and imaginary roots, stating the multiplicity of each.
19) f(x) = -5x2 (x - 6)(x + 3)3
A) -3 with multiplicity 1
3 with multiplicity 1
6 with multiplicity 1
B) -3 with multiplicity 3
0 with multiplicity 2
6 with multiplicity 1
C) -3 with multiplicity 3
0 with multiplicity 2
3 with multiplicity 1
6 with multiplicity 1
D) -3 with multiplicity 3
6 with multiplicity 1
19)
Find a polynomial with real coefficients that has the given roots.
20) 0, -3, 8
A) f(x) = x2 + 5x + 24
B) f(x) = x3 - 24x
C) f(x) = x3 + 5x2 - 24x
20)
D) f(x) = x3 - 5x2 - 24x
Use the rational zero theorem as an aid in finding all real and imaginary roots to the equation.
21) x3 - 6x2 + x - 6 = 0
A) -6, 6, i
B) -6, -i, i
C) 6, -i, i
D) -1, 1, 6
B) {- 6, ± 5}
C) {-6, ±5}
D) {- 6, ±5}
Find all real and imaginary solutions.
22) x3 + 6x2 - 5x - 30 = 0
A) {-6, ± 5}
21)
22)
6
Find all real solutions to the equation.
23) x + 13 = x - 7
A) {3}
B) {3, 12}
24)
2x2 + 4x - 21 = x
A) {3, -7}
23)
C) {12}
D) {-9}
B) No solution
C) {7}
D) {3}
B) No solution
1
C)
81
24)
25) x-3/4 = 27
A) {81}
25)
7
D) {-81}
Answer Key
Testname: CA UNIT 2 EXAM FALL 2013 (UPDATED)
1) A
2) D
3) C
4) B
5) C
6) B
7) C
8) D
9) C
10) B
11) A
12) B
13) C
14) D
15) B
16) A
17) B
18) C
19) B
20) D
21) C
22) A
23) C
24) D
25) C
8