College Algebra - Unit 2 Exam - Practice Questions
Note: The actual exam will consist of 20 multiple choice questions and 6
show-your-work questions. Extra questions are provided for practice.
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)
A) not a function
1)
B) function
2)
2)
A) function
B) not a function
1
3)
3)
A) not a function
B) function
4)
4)
A) not a function
B) function
State the degree of the polynomial equation.
5) 3(x + 7)2 (x - 7)3 = 0
A) 2
6) -12x3 - 6x2 - 8x + 4y4 + 4
A) 4
B) 4
C) 3
D) 5
B) 3
C) 10
D) -12
7) f(x) = x5 + 3x 4 - 7
A) 4
B)
C) 5
D) 1
8) f(x) = 8x5 - 3x4 + 1
A) 10
B) 8
C) 5
D) -3
Find the requested composition of functions.
x - 10
and g(x) = 7x + 10, find (f g)(x).
9) Given f(x) =
7
A) 7x + 60
2
6)
7)
8)
9)
C) x -
B) x + 20
5)
10
7
D) x
10) f(x) = x2 + 2x + 3,
(f g)(-5)
A) 349
11) f(x) =
x-5
,
10
g(x) = x2 + 2x - 4
B) 363
C) 160
D) 146
g(x) = 10x + 5
(g f)(x)
A) 10x + 45
10)
B) x -
11)
1
2
C) x + 10
Find the domain and range.
12) {(10, 5), (-9, 2), (-8, 7), (6, -4)}
A) D = {2, 5, -4, 7}; R = {-9, 10, 6, -8}
C) D = {-9, 10, 6, -8}; R = {2, 5, -4, 7}
D) x
B) D = {-9, 10, 6, -8}; R = { 5, -4, 7}
D) D = {-9, 10, 6, -8}; R = {2, -5, 5, -4, 7}
13) f(x) =3(x-6)2 -12
A) D = (- , ) , R = [-12, )
C) D = (- , -6) (-6, ) , R = [-12, )
B) D = (- , 6) (6, ) , R = [0, )
D) D = (- , ) , R = [-6, )
14) y = x+2
A) D = (- , ); R = (- , )
C) D = [-2, ); R = [0, )
B) D = (- , ); R = [-2, )
D) D = [0, ); R =[0, )
15)
12)
13)
14)
15)
A) domain: (- , -4) or (-4, )
range: (- , 1) or (1, )
C) domain: (- , )
range: (- , 1]
B) domain: (- , )
range: (- , )
D) domain: (- , -4]
range: (- , 1]
3
16)
16)
A) domain: (- , )
range: [0, 6]
B) domain: (- , )
range: [3, 6]
C) domain: [3, 6]
range: (- , )
D) domain: [0, 6]
range: (- , )
Find the domain of the composite function f g.
6
21
,
g(x) =
17) f(x) =
x+7
x
17)
A) (- , -3) or (-3, 0) or (0, )
C) (- , -7) or (-7, -3) or (-3, 0) or (0, )
18) f(x) = 4x + 4;
A) [-1, )
g(x) =
x
B) (- , -7) or (-7, 0) or (0, )
D) (- , )
B) (- , )
C) (- , -1] or [0, )
Solve the absolute value equation or indicate that the equation has no solutions.
19) 7x + 6 + 1 = -6
13 1
1 13
13
,,
A) B)
C) 7
7
7 7
7
20) x - 7 = 3
A) {-4, 10}
B) {4, 10}
C) {-10}
D) [0, )
18)
19)
D) No Solutions
D) No Solutions
20)
Solve the absolute value inequality. Use interval notation to express the solution set and graph the solution set on a
number line.
21) x < 4
21)
A) [-4, 4]
B) (- , -4]
[4, )
C) (-4, 4)
D) (- , -4)
(4, )
4
22) |x - 3|
22)
0
A) (3, )
B) {3}
C) (-3, 3)
D) (- , )
23) |x - 2| + 5 9
23)
A) (-2, 6)
B) [-2, 6]
C) (- , -2]
[6, )
D) [-2, 9]
24)
11y + 22
< 11
2
24)
A) (- , -4)
(4, )
B) (-4, 4)
C) (- , -4)
(0, )
D) (-4, 0)
5
Graph the function.
x+3
25) f(x) = -8
-x + 4
if -7 x < 3
if x = 3
if x > 3
25)
A)
B)
C)
D)
Based on the graph, find the range of y = f(x).
4
if -5 x < -3
|x|
if -3 x < 7
f(x)
=
26)
3
x
if 7 x 13
A) [0, 7]
26)
C) [0,
B) [0, 7)
6
3
13]
D) [0, )
Graph the function.
27) f(x) = -x - 1
-1
A)
for x < 0
for x 0
27)
B)
C)
D)
Use the Rational Zero Theorem to list all possible rational zeros for the given function.
28) f(x) = x5 - 6x2 + 3x + 6
A) ± 1, ± 3, ± 2, ± 6
B) ± 1, ±
1
1
1
, ± , ± , ± 3, ± 2, ± 6
3
2
6
C) ± 1, ± 3, ± 2
D) ± 1, ±
1
1
1
,± ,±
3
2
6
29) f(x) = -2x3 + 4x2 - 3x + 8
1
A) ± , ± 1, ± 2, ± 4, ± 8
2
C) ±
1
1
B) ± , ± , ± 1, ± 2, ± 4, ± 8
4
2
1
, ± 1, ± 2, ± 4
2
D) ±
30) f(x) = 11x3 - x2 + 3
1
3
,±
, ± 1, ± 3, ± 11
A) ±
11
11
C) ±
D) ±
7
29)
1
1
1
, ± , ± , ± 1, ± 2, ± 4, ± 8
8
4
2
1
11
, ± 1, ± 11
B) ± , ±
3
3
1
3
,±
, ± 1, ± 3
11
11
28)
1
1
, ± , ± 1, ± 3, ± 11
11
3
30)
31) f(x) = 3x4 + 2x 3 - 6x2 + 6x - 12
1
2
3
A) ±1, ± 2, ± 3, ± 6, ± 12, ± , ± , ±
3
3
4
B) ±1, ± 2, ± 3, ± 4, ± 6, ± 12, ±
C) ± 1, ± 3, ±
31)
1
2
4
, ± , ±
3
3
3
1
3
1
1
3
1
1
, ± , ± , ± , ± ,± ,±
2
2
3
4
4
6
12
D) ±1, ± 2, ± 3, ± 4, ± 6, ± 12, ±
1
3
1
1
3
1
1
, ± , ± , ± , ± ,± ,±
2
2
3
4
4
6
12
32) Solve the equation 3x3 - 34x2 + 101x - 30 = 0 given that 5 is a zero of f(x) = 3x3 - 34x2 + 101x - 30.
1
1
A) 5, -1, - 2
B) 5, 6,
C) 5, -6, D) 5, 1, 2
3
3
For the given functions f and g , perform the indicated operation.
g(x) = x2 + 2x - 4
33) f(x) = x2 - 2x + 2,
(f g)(-4)
A) 670
B) 10
C) 70
34) (x3 - 1) divided by (x - 1)
A) Q: x3 + x2 + x + 1; R: 0
g(x) = 6x - 9
35) f(x) = 5x - 8,
Find fg.
A) 30x2 - 57x + 72
B) 30x2 + 72
36) f(x) = 5x - 5,
Find f - g.
A) 2x - 3
33)
D) 730
B) Q: x3 + x2 + x + 1; R: x - 1
D) Q: x2 + x + 1; R: 0
C) Q: x2 + x + 1; R: x - 1
32)
34)
35)
C) 30x2 - 93x + 72
D) 11x2 - 93x - 17
36)
g(x) = 7x - 8
B) -2x + 3
C) 12x - 13
D) -2x - 13
Solve the problem.
37) Suppose that a rectangular yard has a width of x and a length of 6x. Write the perimeter P as a
function of x.
A) P = 14x 2
B) P = 6x2
C) P = 14x
D) P = 7x
37)
38) A rectangular playground is to be fenced off and divided in two by another fence parallel to one
side of the playground. 480 feet of fencing is used. Find the dimensions of the playground that
maximize the total enclosed area.
A) 80 ft by 120 ft
B) 40 ft by 180 ft
C) 120 ft by 120 ft
D) 60 ft by 120 ft
38)
39) The profit that the vendor makes per day by selling x pretzels is given by the function
P(x) = -0.002x2 + 1.4x - 50. Find the number of pretzels that must be sold to maximize profit.
39)
A) 700 pretzels
B) 195 pretzels
C) 0.7 pretzels
8
D) 350 pretzels
Find a polynomial equation with real coefficients that has the given roots.
40) 0, -5, 3
A) x3 - 15x = 0
B) x3 - 2x2 - 15x = 0
C) x3 + 2x2 - 15x = 0
40)
D) x2 - 2x + 15 = 0
Find an nth degree polynomial function with real coefficients satisfying the given conditions.
1
41) n = 4; 3, , and 1 + 3i are zeros; f(1) = -54
2
A) f(x) = 6x4 - 33x3 + 111x2 - 228x + 90
C) f(x) = 3x4 - 33x3 + 111x2 - 228x + 90
41)
B) f(x) = -4x4 + 22x3 - 74x2 + 152x - 60
D) f(x) = 2x4 - 11x3 + 37x2 - 228x + 90
42) n = 3; - 6 and i are zeros; f(-3) = 60
A) f(x) = 2x3 + 12x 2 - 2x - 12
42)
B) f(x) = -2x3 - 12x2 + 2x + 12
C) f(x) = -2x3 - 12x2 - 2x - 12
D) f(x) = 2x3 + 12x 2 + 2x + 12
Write the equation of the graph after the indicated transformation(s).
43) The graph of y = x is translated 4 units to the right.
A) y = x + 4
B) y = x - 4
C) y =
43)
x +4
D) y =
x-4
44) The graph of y = x is vertically stretched by a factor of 3.5. This graph is then reflected across the
x-axis. Finally, the graph is shifted 0.51 units downward.
A) y = -3.5 x - 0.51
B) y = 3.5 x - 0.51
C) y = 3.5 x - 0.51
D) y = 3.5 -x - 0.51
For the pair of functions, perform the indicated operation.
45) f(x) = 7x + 6, g(x) = 4x + 7
Find (fg)(x).
A) 28x2 + 73x + 42
B) 28x2 + 42
44)
45)
C) 11x2 + 73x + 13
9
D) 28x2 + 31x + 42
Use transformations of the graph of f(x) =
46) g(x) = - x + 2 + 2
x to graph the given function.
46)
A)
B)
C)
D)
10
47) g(x) = -
47)
x+1-1
A)
B)
C)
D)
11
48) g(x) =
1
x+2 -3
3
48)
A)
B)
C)
D)
12
49) g(x) = -(x + 4)3 + 3
49)
A)
B)
C)
D)
13
The following problems will be graded based on HOW MUCH WORK YOU SHOW. No work = No credit. If you use
your calculator to solve these questions, you must write down your preliminary work and sketch any graphs used to
answer the question.
Identify the interval where the function is decreasing or increasing as requested
50) Decreasing
51) Decreasing
50)
51)
Identify the intervals where the function is changing as requested.
52) Increasing
14
52)
Graph the function.
53) f(x) = -x + 3
2x - 3
if x < 2
if x 2
53)
Evaluate the piecewise function.
54) f(x) = 3x + 2 if x < -4 , determine f(-1)
-2x + 4 if x -4
54)
Graph the function.
55) f(x) = x - 1
5
55)
if x < 1
if x 1
Evaluate the piecewise function.
x2 + 7
if x 6
; h(6)
56) h(x) = x - 6
x+5
56)
if x = 6
Use synthetic division or long division to find the quotient and remainder when the first polynomial is divided by the
second.
57) (x2 - 2x + 7) divided by (x - 4)
57)
58)
x4 + 3x3 + x2 + 5x + 3
x+1
58)
15
59) (3x5 + 4x4 - 2x3 + x2 - x + 18) ÷ (x + 2)
59)
Find all of the real and imaginary zeros for the polynomial function.
60) f(x) = x3 - 8x2 + x - 8
60)
61) f(x) = x3 + 5x2 + 3x - 1
61)
62) f(x) = 3x4 - 16x3 + 56x2 - 56x + 13
62)
For the given functions f and g , find the indicated operation
g(x) = x2 - 2x + 2
63) f(x) = x2 + 2x + 2,
(f g)(4)
64) f(x) = 2x - 2 ,
(f/g)(-2)
g(x) = 3x2 + 14x + 2
63)
64)
16
Answer Key
Testname: CA UNIT 2 PRACTICE EXAM SPRING 2015
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
27)
28)
29)
30)
31)
32)
33)
34)
35)
36)
37)
38)
39)
40)
41)
42)
43)
44)
45)
46)
47)
48)
49)
50)
B
B
B
A
D
A
C
C
D
D
D
C
A
C
C
A
A
D
D
B
C
D
B
D
A
B
B
A
A
C
B
B
B
D
C
B
C
A
D
C
A
D
D
A
A
A
C
B
C
(-3, -2)
51) (5, 12)
52) (-2, -1) or (3, )
53)
54) 6
55)
56) 11
57) Q: x + 2; R: 15
58) x3 + 2x2 - x + 6 -
3
x+1
59) 3x4 - 2x3 + 2x2 + 3x + 5 +
60) 8, -i, i
61) {-1, -2 + 5, -2 - 5}
1
62) {1, , 2 + 3i, 2 -3i}
3
63) 122
3
64)
7
17
8
x+2