Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine whether the equation defines y as a function of x.
1) x + y = 9
A) y is a function of x
B) y is not a function of x
2) 2x + 4y = 5
A) y is a function of x
B) y is not a function of x
3) x2 + y = 81
A) y is a function of x
B) y is not a function of x
4) x + y2 = 49
A) y is a function of x
B) y is not a function of x
Evaluate the function at the given value of the independent variable and simplify.
5) f(x) = -3x - 8; f(-2)
A) -2
B) -11
C) 14
6) f(x) = x2 - 1;
A) x2 + 4
f(x - 2)
7) h(x) = x - 2 ;
A) 11
h(13)
8) f(x) =
A)
x3 + 7
;
x2 - 2
11
2
1)
2)
3)
4)
D) 22
B) x2 - 3
C) x2 - 4x + 3
D) x2 - 4x + 4
B) 15
C) -15
D) -11
f(-2)
5)
6)
7)
8)
B) -
1
4
C) -
1
2
D) - 4
Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x.
9)
A) function
B) not a function
1
9)
10)
10)
A) function
B) not a function
11)
11)
A) function
B) not a function
Use the graph to find the indicated function value.
12) y = f(x). Find f(3).
A) -3
12)
B) 1.5
C) 9
2
D) 3
The graph below shows the percentage of students enrolled in the College of Engineering at State University. Use the
graph to answer the question.
13) If f represents the function, find f(2000).
A) approximately 24%
C) approximately 31%
B) approximately 29%
D) approximately 25.5%
14) If f(x) = 20%, what year is represented by x?
A) 1985
B) 1975
C) 1980
13)
D) 1990
Use the graph to determine the function's domain and range.
15)
A) domain: (- , )
range: (- , )
C) domain: [-1, )
range: [-4, )
15)
B) domain: (- , -1) or (-1, )
range: (- , -4) or (-4, )
D) domain: (- , )
range: [-4, )
3
14)
16)
16)
A) domain: [0, )
range: [0, )
B) domain: [0, )
range: [-1, )
C) domain: (- , )
range: [-1, )
D) domain: [0, )
range: (- , )
17)
17)
A) domain: (- , )
range: [0, 4]
B) domain: [0, 4]
range: (- , )
C) domain: (- , )
range: [3, 4]
4
D) domain: [3, 4]
range: (- , )
Identify the intervals where the function is changing as requested.
18) Constant
A) (-1, 0)
C) (3, )
18)
B) (- , 0)
D) (- , -1) or (3, )
19) Increasing
A) (-2, )
19)
B) (-2, 0)
C) (3, )
D) (3, 6)
20) Decreasing
A) (0, -2)
20)
B) (-3, -2)
C) (- , -2)
5
D) (- , -3)
The graph of a function f is given. Use the graph to answer the question.
21) Find the numbers, if any, at which f has a relative maximum. What are the relative maxima?
21)
A) f has a relative maximum at x = -1 and 1; the relative maximum is 0
B) f has a relative maximum at x = 0; the relative maximum is 3
C) f has a relative maximum at x = 1; the relative maximum is 3
D) f has no relative maximum
22) Find the numbers, if any, at which f has a relative minimum. What are the relative minima?
22)
A) f has a relative minimum at x = 0; the relative minimum is 3
B) f has a relative minimum at x = -1; the relative minimum is 0
C) f has a relative minimum at x = -1 and 1; the relative minimum is 0
D) f has no relative minimum
Determine whether the given function is even, odd, or neither.
23) f(x) = 5x2 + x4
A) Odd
B) Neither
C) Even
24) f(x) = x3 - 4x
A) Neither
B) Even
C) Odd
25) f(x) = x4 - x3
A) Even
B) Odd
C) Neither
6
23)
24)
25)
Use possible symmetry to determine whether the graph is the graph of an even function, an odd function, or a function
that is neither even nor odd.
26)
26)
A) Odd
B) Even
C) Neither
27)
27)
A) Neither
B) Even
C) Odd
Evaluate the piecewise function at the given value of the independent variable.
28) f(x) = 3x + 1 if x < -1 ; f(2)
-2x - 5 if x -1
A) -3
B) -9
C) 1
29) g(x) =
x2 + 5
x+3
x-7
A) -5
if x
-3
if x = -3
28)
D) -8
29)
; g(-5)
B) - 15
C) 0
Graph the function.
7
D) -12
30) f(x) = x + 1
4
if x < 1
if x 1
30)
A)
B)
C)
D)
Find and simplify the difference quotient
31) f(x) = 6x - 2
-4
A) 6 +
h
f(x + h) - f(x)
, h 0 for the given function.
h
12(x - 2)
C) 6 +
h
B) 0
8
31)
D) 6
32) f(x) = 7x2
32)
A) 7(2x+h)
14
+ x + 7h
B)
h
C) 7
D)
7(2x2 + 2xh + h 2 )
h
Begin by graphing the standard quadratic function f(x) = x 2 . Then use transformations of this graph to graph the given
function.
33) h(x) = (x - 7)2 - 5
33)
34) h(x) = -(x + 3)2 + 3
34)
9
Begin by graphing the standard cubic function f(x) = x 3. Then use transformations of this graph to graph the given
function.
35) h(x) = (x + 3)3 - 3
35)
Use the graph of the function f, plotted with a solid line, to sketch the graph of the given function g.
36) g(x) = -f(x - 1) + 2
36)
y = f(x)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the domain of the function.
37) f(x) = -9x + 1
A) [-1, )
38) f(x) =
B) (- , )
C) (- , 0)
D) (0, )
x2
x2 + 10
B) (- , -10)
D) (- , )
39) f(x) = 10 - x
A) (- , 10]
C) (- , 10]
(-10, )
39)
B) (- , 10) (10, )
D) (- , 10) ( 10, )
x
x-9
A) (- , 9)
37)
38)
A) (-10, )
C) (- , 0) (0, )
40)
(0, )
40)
(9, )
B) [9, )
C) (- , )
10
D) (9, )
Given functions f and g, perform the indicated operations.
g(x) = 9x - 8
41) f(x) = 2x - 6,
Find f - g.
A) 11x - 14
B) -7x + 2
41)
C) -7x - 14
D) 7x - 2
42) f(x) = 9x2 - 7x, g(x) = x2 - 5x - 14
f
Find .
g
A)
9-x
14
43) f(x) = 3 - 5x,
Find f + g.
A) -13x + 8
B)
42)
9x
x+1
C)
9x - 7
-5
D)
9x2 - 7x
2
x - 5x - 14
g(x) = -8x + 5
43)
B) 3x + 8
44) f(x) = 2x + 3, g(x) =
Find fg.
A) (2x + 3)(4x - 5)
C) (4x - 5)( 2x + 3)
C) -5x
D) -8x + 3
16x - 25
44)
B) (2x + 3)(16x - 25)
D) ( 2x + 3)( 16x - 25)
Solve the problem.
45) A firm is considering a new product. The accounting department estimates that the total cost, C(x),
of producing x units will be
C(x) = 95x + 4200.
The sales department estimates that the revenue, R(x), from selling x units will be
R(x) = 105x,
but that no more than 629 units can be sold at that price. Find and interpret (R - C)(629).
A) $1049 profit, income exceeds cost
B) $2090 profit, income exceeds cost
It is worth it to develop product.
It is worth it to develop product.
C) $130,000 profit, income exceeds cost
D) -$2090 loss, cost exceeds income
It is worth it to develop product.
It is not worth it to develop product.
For the given functions f and g , find the indicated composition.
46) f(x) = 17x2 - 6x, g(x) = 8x - 5
(f g)(8)
A) 50,508
B) 58,823
C) 8315
47) f(x) = x2 + 2x + 2,
(f g)(-3)
A) 136
48) f(x) = 3x + 9,
(f g)(x)
A) 15x + 6
45)
46)
D) 61,360
g(x) = x2 - 2x - 3
47)
B) 51
C) 170
D) 17
g(x) = 5x - 1
48)
B) 15x + 8
C) 15x + 44
11
D) 15x + 12
49) f(x) =
6
,
x+8
g(x) =
7
8x
49)
(f g)(x)
A)
6x
7 + 64x
B)
48x
7 - 64x
C)
7x + 56
48x
D)
48x
7 + 64x
Determine which two functions are inverses of each other.
x-2
x+2
g(x) = 3x - 2
h(x) =
50) f(x) =
3
3
A) f(x) and g(x)
50)
B) f(x) and h(x)
C) g(x) and h(x)
D) None
Find the inverse of the one-to-one function.
6x - 7
51) f(x) =
5
5x - 7
A) f-1 (x) =
6
B) f-1 (x) =
51)
5
6x - 7
C) f-1 (x) =
5
6x + 7
5x + 7
D) f-1 (x) =
6
52) f(x) = (x + 6)3
52)
A) f-1 (x) =
C) f-1 (x) =
53) f(x) =
3
x-6
B) f-1 (x) =
x - 216
D) f-1 (x) =
3
3
x-6
x+6
x-7
A) f-1 (x) = x2 + 7
B) f-1 (x) = x2 - 7
C) f-1 (x) = x + 7
Does the graph represent a function that has an inverse function?
54)
A) Yes
B) No
12
1
D) f-1 (x) =
2
x +7
53)
54)
55)
55)
A) Yes
B) No
Use the graph of f to draw the graph of its inverse function.
56)
56)
57)
57)
13
Answer Key
Testname: MAC1105_PE2
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2)
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A
A
A
B
A
C
A
C
A
B
A
B
B
A
D
B
A
D
C
B
B
C
C
C
C
C
C
B
B
B
D
A
14
Answer Key
Testname: MAC1105_PE2
34)
35)
36)
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48)
49)
50)
B
D
C
D
B
D
A
D
B
B
C
A
D
C
15
Answer Key
Testname: MAC1105_PE2
51)
52)
53)
54)
55)
56)
D
B
A
B
A
57)
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