College Algebra - Unit 2 Exam - Spring 2015
Printed Name___________________________________
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.
Points: 2
1)
A) Yes
1)
B) No
State the degree of the polynomial equation.
Points: 2
2) 2(x + 7)2 (x - 7)3 = 0
A) 4
B) 5
C) 2
D) 3
Find the requested composition of functions.
Points: 2
x-5
and g(x) = 4x + 5, find (f g)(x).
3) Given f(x) =
4
A) x -
5
4
2)
3)
B) x + 10
C) x
Find the domain and range.
Points: 2
4) {(12, -8), (-4, 2), (-2, -7), (-3, 9)}
A) D = {2, -7, 9, -8}; R = {-4, -2, -3, 12}
C) D = {-4, -2, -3, 12}; R = {2, -7, 9, -8}
D) 4x + 15
B) D = {-4, -2, -3, 12}; R = { -7, 9, -8}
D) D = {-4, -2, -3, 12}; R = {2, 8, -7, 9, -8}
4)
Points: 2
5) f(x) =3(x-6)2 -12
A) D = (- , -6) (-6, ) , R = [-12, )
C) D = (- , ) , R = [-12, )
B) D = (- , ) , R = [-6, )
D) D = (- , 6) (6, ) , R = [0, )
Points: 2
6) y = x+5
A) D = [0, ); R =[0, )
C) D = (- , ); R = [-5, )
B) D = (- , ); R = (- , )
D) D = [-5, ); R = [0, )
1
5)
6)
Solve the absolute value equation or indicate that the equation has no solutions.
Points: 2
7) 3x + 7 + 3 = 1
5
5
A) - 3,
B) - , 3
C) - 3
3
3
Points: 2
8) x - 5 = 8
A) {-13}
B) {-3, 13}
C) {3, 13}
7)
D) No Solutions
D) No Solutions
8)
Solve the absolute value inequality. Use interval notation to express the solution set and graph the solution set on a
number line.
Points: 2
9) x < 2
9)
A) [-2, 2]
C) (- , -2]
B) (-2, 2)
D) (- , -2)
[2, )
2
(2, )
Graph the function.
Points: 2
10) f(x) = -x - 3
-3
A)
for x < 0
for x 0
10)
B)
C)
D)
Use the Rational Zero Theorem to list all possible rational zeros for the given function.
Points: 2
11) f(x) = -2x3 + 4x2 - 3x + 8
1
A) ± , ± 1, ± 2, ± 4
2
C) ±
1
1
1
B) ± , ± , ± , ± 1, ± 2, ± 4, ± 8
8
4
2
1
1
, ± , ± 1, ± 2, ± 4, ± 8
4
2
D) ±
11)
1
, ± 1, ± 2, ± 4, ± 8
2
Points: 2
12) Solve the equation 3x3 - 22x2 + 5x + 14 = 0 given that 1 is a zero of f(x) = 3x3 - 22x2 + 5x + 14.
7
2
7
2
A) 1, 2, B) 1, -2,
C) 1, -7,
D) 1, 7, 3
3
3
3
For the given functions f and g , perform the indicated operation.
Points: 2
13) f(x) = x2 - 2x - 2, g(x) = x2 - 2x - 5
(f g)(-4)
A) 438
B) 444
C) 321
3
12)
13)
D) 315
Points: 2
14) (x3 - 1) divided by (x - 1)
A) Q: x3 + x2 + x + 1; R: x - 1
14)
B) Q: x2 + x + 1; R: 0
D) Q: x3 + x2 + x + 1; R: 0
C) Q: x2 + x + 1; R: x - 1
Solve the problem.
Points: 2
15) Suppose that a rectangular yard has a width of x and a length of 2x. Write the perimeter P as a
function of x.
A) P = 6x
B) P = 6x2
C) P = 3x
D) P = 2x2
Use the graph to determine the function's domain and range.
Points: 2
16)
A) domain: [0, )
range: [0, )
B) domain: (- , )
range: [-1, )
16)
C) domain: [0, )
range: (- , )
D) domain: [0, )
range: [-1, )
Find a polynomial equation with real coefficients that has the given roots.
Points: 2
17) 0, -4, 8
A) x3 + 4x2 - 32x = 0
B) x3 - 4x2 - 32x = 0
C) x3 - 32x = 0
15)
17)
D) x2 + 4x + 32 = 0
Write the equation of the graph after the indicated transformation(s).
Points: 2
18) The graph of y = x is translated 8 units to the right.
A) y = x + 8
B) y = x + 8
C) y =
18)
x -8
D) y =
x-8
Points: 2
19) The graph of y = x is vertically stretched by a factor of 7.5. This graph is then reflected across the
x-axis. Finally, the graph is shifted 0.45 units downward.
A) y = 7.5 x - 0.45
B) y = 7.5 x - 0.45
C) y = 7.5 -x - 0.45
D) y = -7.5 x - 0.45
4
19)
For the pair of functions, perform the indicated operation.
Points: 2
20) f(x) = 8x - 8, g(x) = 5x + 3
Find (fg)(x).
A) 13x2 - 16x - 5
B) 40x2 - 37x - 24
Use transformations of the graph of f(x) =
Points: 2
21) g(x) = - x + 2 - 1
20)
C) 40x2 - 24
D) 40x2 - 16x - 24
x to graph the given function.
21)
A)
B)
C)
D)
5
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
Points: 10
22) Decreasing
22)
Evaluate the piecewise function.
Points: 10
23) f(x) = -3x + 4 if x < -3 , determine f(-2)
5x - 3 if x -3
23)
Use synthetic division or long division to find the quotient and remainder when the first polynomial is divided by the
second.
Points: 10
24) (x2 - 2x + 7) divided by (x - 4)
24)
Find all of the real and imaginary zeros for the polynomial function.
Points: 10
25) f(x) = x3 - 7x2 + x - 7
25)
Points: 10
26) Find (f/g)(-5) given f(x) = 5x - 5 and g(x) = 5x2 + 14x + 3.
6
26)
Answer Key
Testname: CA UNIT II EXAM SPRING 2015V2
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A
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C
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D
B
B
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D
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B
A
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B
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D
D
B
(-3, -2)
-13
Q: x + 2; R: 15
7, -i, i
15
26) 29
7