Calculus with applications 10th edition lial test bank

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine whether the rule defines y as a function of x.
1)
X
Y
1) _______

A) Function

B) Not a function

2)

2) _______
X

Y

A) Function

B) Not a function

3)

3) _______
X

A) Function
4)

Y

B) Not a function


4)

__
__
__
_

A) Function

B) Not a function

5)

5) _______

A) Function

B) Not a function

6) y =
+4
A) Function

6) _______
B) Not a function

7) x =
+8
A) Function

7) _______
B) Not a function

Give the range for the function if the domain is {-2, -1, 0, 1, 2}.
8) y = x + 7
A) {-2, -1, 0, 1, 2}
B) {5, 6, 7, 8, 9}
C) {-5, -3, -1, 1, 3}
9) y = 2x - 1
A) {-2, -1, 0, 1, 2}
C) {-4, -3, -2, -1, 0}

9) _______
B) {-5, -3, -1, 1, 3}
D) {-3, -1, 1, 3, 5}

10) 3x + y = 11
A) {-5, -8, -11, -14, -17}
C) {13, 11, 9, 7, 5}

B) {17, 14, 11, 8, 5}
D) {-5, -7, -9, -11, -13}

11) 5x - y = 2
A) {-12, -7, -2, 3, 8}
C) {-10, -5, 0, 5, 10}

B) {-12, 0, 12}
D) {-10, 0, 10}

12) y = x(x - 1)
A) {-8, -4, 0, 4, 8}
13) y = x2
A) {0, 1, 2}
14) y = - 4x2
A) {-16, -4, 0}

8) _______
D) {5, 7, 9, 11, 13}

10) ______

11) ______

12) ______
B) {0, 2, 6}

C) {-6, -2, 0, 2, 6}

D) {0, 4, 8}
13) ______

B) {-4, -1, 0, 1, 4}

C) {-2, -1, 0, 1, 2}

D) {0, 1, 4}
14) ______

B) {-4, 0, 4}

C) {0, 4, 16}

15)

D) {-16, 0, 16}
15) ______

y=
A)

B)


C)

D)

16)

16) ______
y=
A)

B)

C)

D)

17)

17) ______
y=
A)

B)

C)

D)

Give the domain of the function.
18) f(x) = 3x + 1
A) [-1, ∞)

18) ______
B) (-∞, ∞)

19) f(x) =
A) [0, ∞)

C) (-∞, 0) ∪ (0, ∞)

D) (0, ∞)
19) ______

B)
∪

C) (-∞, ∞)

20) f(x) = 5x2 + 3x + 1
A) (-∞, 0) ∪ (0, ∞)

D)

20) ______
B) (0, ∞)

C) (-∞, ∞)

D) (-∞, 0)

21)

21) ______
f(x) =
A) (-∞, 7) ∪ (7, 3) ∪ (3, ∞)
C) (-∞, -3) ∪ (-3, -7) ∪ (-7, ∞)

22) f(x) =
A) [4, ∞)

B) (-∞, -7) ∪ (-7, 3) ∪ (3, ∞)
D) (-∞, -3) ∪ (-3, 7) ∪ (7, ∞)

22) ______

B) (-∞, - 4]

23) f(x) =
A) [0, 16]
C) (-∞, 16]

C) [- 4, ∞)

D) (-∞, 4]
23) ______

B) (-∞, ∞)
D) (-∞, 16) ∪ (16, ∞)

24)

24) ______
f(x) =
A) (-1, 8)

25)

g(z) =
A) (- 1, 1)

B) (-∞, -1] ∪ [8, ∞)

C) (-∞, -1) ∪ (8, ∞)

D) (-∞, -1] ∪ (8, ∞)
25) ______

B) (-∞, ∞)

C) [- 1, 1]

D) [0, ∞)


26)

26) ______
f(x) =
A) (7, 2)

B) (-∞, -7) ∪ (2, ∞)

C) (-∞, 2) ∪ (7, ∞)

D) (-∞, ∞)

Give the domain and range of the function.
27)

A) Domain [-5, 4] ; Range [-4, 4]
C) Domain [-4, 4) ; Range (-5, 4]

27) ______

B) Domain (-5, 4) ; Range [-2, 4)
D) Domain (-5, 4] ; Range [-4, 4)

28)

28) ______

A) Domain (-∞, ∞) ; Range [-2, 4]
C) Domain (-∞, ∞) ; Range [-2, ∞)
29)

B) Domain (-∞, ∞) ; Range [0, ∞)
D) Domain (-5, 5) ; Range [-2, 8)
29) ______

A) Domain {-6, 4, 6} ; Range {-8, -4, -1, 1, 4, 8}
B) Domain [-8, 8] ; Range [-6, 6]


C) Domain [-6, 6] ; Range [-8, 8]
D) Domain {-8, -4, -1, 1, 4, 8} ; Range {-6, 4, 6}
30)

30) ______

A) Domain {-4, 8} ; Range {0, 3}
C) Domain = (-4, 8) ; Range (0, 3)
31)

31) ______

A)
B)
C)
D)
32)

B) Domain (-∞, ∞) ; Range (-∞, ∞)
D) Domain [-4, 8] ; Range [0, 3]

Domain (-∞, 0) ∪ (0, ∞) ; Range (-∞, 0) ∪ (0, ∞)
Domain (0, ∞) ; Range [15, ∞)
Domain (-∞, 0) ; Range (-∞, 0)
Domain (-∞, ∞) ; Range [-6, ∞)
32)


______
A) Domain (-∞, ∞) ; Range (-∞, ∞)
C) Domain (-∞, ∞) ; Range [-3, ∞)

B) Domain {-5, -3, 1} ; Range (-∞, ∞)
D) Domain (-∞, ∞) ; Range {-5, -3, 1}

33)

33) ______

A)

B)
C)
D)

Domain (-∞, 6) ∪ (6, ∞) ; Range (-∞, 0) ∪ (0, ∞)
Domain (-∞, ∞) ; Range [0, ∞)
Domain (-∞, 6] ; Range [0, ∞)
Domain [0, ∞) ; Range (-∞, 6]

34)

34) ______

A) Domain (-∞, ∞) ; Range {6}
C) Domain [-7, 7] ; Range {6}

B) Domain (-7, 7) ; Range {6}
D) Domain {6} ; Range (-7, 7)

Use the graph to evaluate the function f(x) at the indicated value of x.
35) Find f(1.5).


35)

___
___

A) 1
C) -2

B) 0
D) None of these are correct.

36) Find f(1.5).

36) ______

A) -1
C) -2

B) 0.5
D) None of these are correct.

Evaluate the function.
37) f(x) = x2 - 5x - 3;
A) -3
38) f(x) = x2 - 3x - 5;
A) 5
39) f(x) = 4x2 - 5x + 6;
A) 0
40) f(x) = (x - 5)(x + 2);
A) -6

Find f(-2).
B) -9
Find f(0).
B) 0
Find f(2).
B) 0

Find f(-1).
B) 18

37) ______
C) 11

D) 17
38) ______

C) 25

D) -5
39) ______

C) 32

D) 12

C) -12

D) 4

40) ______

41)

41) ______
f(x) =
A) 6

;

Find f(-1).
B)

C)

D)
-


42)

42) ______
f(x) =
A) 5

;

Find f(5).
B)

43) f(x) = 3 + 4x + 6;
A) 7a + 6

Find f(a).
B) 3

44) f(x) = (x - 1)(x + 4);
A) (a - 1)(a - 4)

Find f(a).
B)

C)

43) ______
+ 4a

C) -3

+ 2x - 2;
- 6rh - 3
-3

C) 3

D) 7a

+ 4a + 6

44) ______
+4

45) f(x) = 5x2 - 3x + 2; Find f(t - 1).
A) 5 - 13t + 10
B) -13
46) f(x) = -3
A) -3

D)

C)

D) (a - 1)(a + 4)

-4

45) ______
+ 5t + 10

C) 5

D) 5

+ 7t + 4

46) ______

Find f(r + h).
+ 2r + 2h - 2

+ 2r + 2h - 2

B) -3
D) -3

- 3rh - 3
-3

+ 2r + 2h - 2

- 4r - 4h - 2

Evaluate the function for the given value.
47)

f(x) =
A) 12

; f
B) - 6

- 13t + 4

47) ______

C) 0

D)
-

48)

48) ______

f(x) =
A) 0

; f(5)

B) 60

C)

D) 12

49)

49) ______
f(x) =
A) 2 if a ≠ 7, 9 if a = 7

; f(a)
B)
if a ≠ 7, 9 if a = 7
D) 0 if a ≠ 7, 9 if a = 7

C)
if a = 7, 9 if a ≠ 7
50)

50) ______
f(x) =
A)

; f
B)
if m ≠

C)

, 9 if m =

if m ≠

, 9 if m =


D)
if m
≠

, 9 if m =

2
if
m
≠
,
9
if
m
=

Find

.
51) f(x) = 2x - 13
A) 13

51) ______
B) - 2h

52) f(x) = 6 + 12x - 13
A) 12x + 12

C) 2

D)

52) ______
B)

12xh + 12h + 12
D) 6x + 6 + 12h

C) 12x + 12 + 6h
53)

53) ______
f(x) =
A)

B)

C)

D)

54) f(x) = 14 - 2

A) -3
C) - 2(3

54) ______

+ 3xh +

B) - 2( - xh )
D) - 2(3 - 3x - h)

)

55)

55) ______
f(x) =
A)

B)
-

C) 0
-

D)
-

56)

56) ______

f(x) =
A)

B)
-

C)

D)

Decide whether the graph represents a function.


57)

57) ______

A) Function

B) Not a function

58)

58) ______

A) Function

B) Not a function

59)

59) ______

A) Function
60)

B) Not a function


60)

A) Function

___
___

B) Not a function

61)

61) ______

A) Function

B) Not a function

62)

62) ______

A) Function
63)

B) Not a function


63)

___
___

A) Function

B) Not a function

64)

64) ______

A) Function

B) Not a function

Classify the function as even, odd, or neither.
65) f(x) = 4x
A) Even
B) Odd
66) f(x) = 5
A) Even
67) f(x) = -4

A) Even
68) f(x) = -5 A) Even
69) f(x) = - 7
-4
A) Even
70) f(x) = 7 - 4
A) Even

65) ______
C) Neither
66) ______

B) Odd

C) Neither
67) ______

B) Odd

C) Neither
68) ______

B) Odd

C) Neither
69) ______

B) Odd

C) Neither

70) ______

B) Odd

C) Neither


71)

71) ______
f(x) =
A) Even

B) Odd

C) Neither

72)

72) ______
f(x) =
A) Even

B) Odd

73) f(x) = -2 + 4x
A) Even

C) Neither
73) ______

B) Odd

74) f(x) =
A) Even

C) Neither
74) ______

B) Odd

C) Neither

Solve the problem.
75) The table shows the estimated number of pounds of summer flounder harvested in North
Carolina each year from 1992-1998. Let y = f(x) represent the number of flounder (in millions of
pounds) and x represent the years. What is the dependent variable?

A)
B)
C)
D)

75) ______

The number of hurricanes striking the N.C. coast in the given year
None of these are correct.
Years
Millions of pounds of flounder

76) A state park charges

per day or fraction of a day to rent a tent site, plus a fixed

park

76) ______

maintenance fee. Let T(x) represent the cost to stay in a tent site for x days. Find
A) $94.60
77) A hummingbird adds

B) $91.00

C) $103.00

D) $84.00

grams per day to its base body weight of grams during the spring

77) ______

migration. Let T(x) represent the hummingbird's weight after x days. Find
A) 26 g

B) 44 g

C) 31 g

D) 37.50 g

78) Sue wants to put a rectangular garden on her property using 80 meters of fencing. There is a
river that runs through her property so she decides to increase the size of the garden by using
the river as one side of the rectangle. (Fencing is then needed only on the other three sides.) Let x
represent the length of the side of the rectangle along the river. Express the garden's area as a
function of x.

78) ______


A)

B)

A(x) = 40x C) A(x) = 40 - x

A(x) = 39x D) A(x) = 41x - 2

79) A farmer has 1000 yards of fencing to enclose a rectangular garden. Express the area A of the
rectangle as a function of the width x of the rectangle. What is the domain of A?
A) A(x) = - + 1000x; {x|0 < x < 1000}
B) A(x) =
+ 500x; {x|0 < x < 500}
C) A(x) = -

+ 500x; {x|0 < x < 500}

D) A(x) = -

79) ______

+ 500x; {x|0 < x < 1000}

80) Suppose a life insurance policy costs $32 for the first unit of coverage and then $8 for each
additional unit of coverage. Let C(x) be the cost for insurance of x units of coverage. What will
10 units of coverage cost?
A) $80
B) $48
C) $112
D) $104

80) ______

81) The graph shows the relationship between the area A of a rectangle and the length L, if the
width is fixed. Find the area if the length is 8 cm.

81) ______

A) 54 cm2

B) 45 cm2

C) 90 cm2

D) 72 cm2

82) The territorial area of an animal is defined to be its defended region, or exclusive region. For
example, a rhinoceros has a certain region over which it is ruler. The area T of that region, in
acres, can be approximated by the function

82) ______

T=
,
where W is the weight of the animal, in tons. Find the approximate territorial area of a
rhinoceros who weights 4.6 tons. Round to the nearest hundredth.
A) 17.62 acres
B) 0.05 acres
C) 0.06 acres
D) 18.24 acres
83) When pouring water from one five gallon bucket to another, a person tends to pour at a faster
rate at first and then slow down in order not to spill. The amount of water left in the original
bucket can be approximated by
where f(t) is measured in gallons and t is the time spent pouring in seconds. Find the
approximate amount of water left in the original bucket after 6 seconds of pouring. Round to the

nea 83)
rest
hun
dre
dth.


______
A) 2.66 gal

B) 2.34 gal

C) 4.4 gal

Match the correct graph to the given function.
84) y = x2 - 6

84) ______

A)

B)

C)

D)

85) y = x2 + 1
A)

C)

D) 4.2 gal

85) ______
B)


D)

86) y =
A)

B)

C)

D)

87) y =
A)

86) ______

87) ______


B)

C)

88) y = (
A)

C)

D)

88) ______

+1
B)

D)

89) y = -(
A)

B)

C)

90) y = A)

89) ______

-1

D)

-4

90) ______


B)

C)

D)

Graph the parabola and give its vertex, axis, x-intercepts, and y-intercepts.
91) f(x) =

+ 10x

A) vertex (5, -25); axis is x = 5;
x-intercepts are 0 and 10; y-intercept is 0

91) ______


B) vertex (-5, 25); axis is x = -5;
no x-intercepts; y-intercept is 50

C) vertex (-5, -25); axis is x = -5;
x-intercepts are 0 and - 10; y-intercept is 0

D) vertex (5, 25); axis is x = 5;
no x-intercepts; y intercept is 50

92) f(x) = -

- 12x


92)

A) vertex (6, 36); axis is x = 6;
x-intercepts are 0 and 12; y-intercept is 0

B) vertex (-6, -36); axis is x = -6;
no x-intercepts; y-intercept is -72

C) vertex (6, - 36); axis is x = 6;
no x-intercepts; y-intercept is -72

D) vertex (-6, 36); axis is x = -6;

___
___


x-intercepts
are 0 and -12;
y-intercept is 0

93) f(x) =

94)

93) ______

+ 12x + 36

A) vertex (6, 36); axis is x = 6;
no x-intercepts; y-intercept is 72

B) vertex (6, 0); axis is x = 6;
x-intercept is 6; y-intercept is 36

C) vertex (-6, 0); axis is x = -6;
x-intercept is -6; y-intercept is 36

D) vertex (-6, 36); axis is x = -6;
no x-intercepts; y-intercept is 72

f(x)


=
+
2x - 8

94)

A) vertex (-1, 9); axis is x = -1;
x-intercepts are 2 and - 4; y-intercept is 8

B) vertex (-1, -9); axis is x = -1;
x-intercepts are 2 and - 4; y-intercept is -8

C) vertex (1, 9); axis is x = 1;
x-intercepts are -2 and 4; y-intercept is 8

___
___


D) vertex (1, -9); axis is x = 1;
x-intercepts are -2 and 4; y-intercept is -8

95) f(x) = -

- 2x + 3

A) vertex (-1, 4); axis is x = -1;
x-intercepts are 1 and - 3; y-intercept is 3

B) vertex (1, -4); axis is x = 1;
x-intercepts are -1 and 3; y-intercept is -3

95) ______


C) vertex (-1, -4); axis is x = -1;
x-intercepts are 1 and - 3; y-intercept is -3

D) vertex (1, 4); axis is x = 1;
x-intercepts are -1 and 3; y-intercept is 3

96) f(x) =

- 6x + 5

A) vertex (-3, 4); axis is x = -3;
x-intercepts are -5 and - 1; y-intercept is -5

96) ______