calculus ch1 a test bank
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ExamName___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the domain and range of the function.
1)
f(x) = 4 -
1)
_______ A)
D (-∞, ∞), R [ 4, ∞)
B)
D (-∞, 4], R (-∞, ∞) C)
D (-∞, ∞), R (-∞, ∞)
D)
D (-∞, ∞), R (-∞, 4] Answer
D
2)
F(t) = - 3
2)
_______ A)
D (-∞, ∞), R [ -3,∞)
B)
D (-∞, ∞), R (-∞, ∞) C)
D [ -9,∞), R [ -3,∞)
D)
D [0, ∞), R (-∞, -3] Answer
A
3)
g(z) = -2 -
3)
_______ A)
D (-∞,0], R [ -2,∞)
B)
D (-∞, ∞), R (-∞, -2] C)
D [0,∞), R (-∞, -2]
D)
D (-∞, -2], R (-∞, ∞) Answer
C
4)
f(x) = -2 +
4)
_______ A)
D [0,∞), R (-∞, ∞)
B)
D (-∞, ∞), R [ -2,∞) C)
D (-∞,0], R (-∞, -2]
D)
D [0,∞), R [ -2,∞) Answer
D
5)
F(t) =
5)
_______ A)
D (-∞,0), R (-∞,0)
B)
D (-∞,∞), R (-∞,∞) C)
D [0,∞), R (-∞,∞)
D)
D (0,∞), R (0,∞) Answer
D
6)
g(z) =
6)
_______ A)
D (-1,∞), R (-∞,0)
B)
D [0,∞), R (-∞,∞) C)
D [1,∞), R (-∞,∞)
D)
D (-∞,-1), R (0,∞) Answer
A
7)
f(x) =
7)
_______ A)
D [0,∞), R
B)
D (-∞,0], R(-∞,0] C)
D [0,∞), R (-∞,∞)
D)
D (-∞,∞), R Answer
A
8)
F(t) =
8)
_______ A)
D (-∞,∞), R (-∞,∞)
B)
D (-∞,0), R (-∞,0) C)
D [0,∞), R [0,∞)
D)
D (0,∞), R (0,∞) Answer
D
9)
g(z) =
9)
_______ A)
D (-∞,∞), R (0, 1)
B)
D (-1, 1), R (-1, 1) C)
D [-1, 1], R [0, 1]
D)
D [0,∞), R (-∞,∞) Answer
C
Determine whether or not the graph is a graph of a function of x. 10)
10)
______ A)
Function
B)
Not a function Answer
A
11)
11)
______ A)
Function
B)
Not a function Answer
A
12)
12)
______ A)
Function
B)
Not a function Answer
B
13)
13)
______ A)
Function
B)
Not a function Answer
B
14)
14)
______ A)
Function
B)
Not a function Answer
A
15)
15)
______ A)
Function
B)
Not a function Answer
A
Find the formula for the function. 16)
Express the perimeter of a square as a function of the square's side length x.
16)
______ A)
p =
B)
p =
C)
p = 4x
D)
p = 6x Answer
C
17)
Express the area of a square as a function of its side length x.
17)
______ A)
A = 4x
B)
A =
C)
A = 2x
D)
A = Answer
B
18)
Express the length d of a square's diagonal as a function of its side length x.
18)
______ A)
d = x
B)
d = x
C)
d = x
D)
d = 2x Answer
C
19)
Express the perimeter of an isosceles triangle with side lengths x, 5x, and 5x as a function of the side length.
19)
______ A)
p = 11x
B)
p = 10x
C)
p = 10
D)
p = 25 Answer
A
20)
Express the area of a circle as a function of its radius r.
20)
______ A)
A = π
B)
A = πr
C)
A = 2πr
D)
A = π Answer
A
21)
Express the volume of a sphere as a function of its radius r.
21)
______ A)
V = π
B)
V = π
C)
V = π
D)
V = π Answer
C
22)
A point P in the first quadrant lies on the graph of the function f(x) = . Express the slope of the line joining P to the origin as a function of x.
22)
______ A)
m =
B)
m = 2x
C)
m =
D)
m = x Answer
D
23)
A point P in the fourth quadrant lies on the graph of the function f(x) = . Express the slope of the line joining P to the origin as a function of x.
23)
______ A)
m =
B)
m = -2x
C)
m = -x
D)
m = x Answer
C
Find the domain and graph the function. 24)
f(x) = 4x + 9
24)
______ A)
D (-∞, ∞)
B)
D (-∞, ∞)
C)
D (-∞, ∞)
D)
D [0, ∞)
Answer
B
25)
g(x) = -7 + 2x - x2
25)
______ A)
D (-∞, ∞)
B)
D (-∞, - 6]
C)
D (-∞, ∞)
D)
D (-∞, ∞)
Answer
A
26)
F(x) =
26)
______ A)
D [0, ∞)
B)
D (-∞, 0)
C)
D (-∞, ∞)
D)
D (-∞, 0]
Answer
D
27)
G(x) =
27)
______ A)
D (-∞, 0)
B)
D (-∞, ∞)
C)
D [0, ∞)
D)
D (-∞, 0]
Answer
B
28)
F(t) =
28)
______ A)
D (-∞, ∞)
B)
D (-∞, 1) ∪ ( 1, ∞)
C)
D (-∞, 0) ∪ (0, ∞)
D)
D (-∞, 1) ∪ ( 1>, ∞)
Answer
B
29)
G(t) =
29)
______ A)
D (-∞, 0) ∪ (0, ∞)
B)
D (-∞, -1) ∪ ( -1, ∞)
C)
D (-∞, -1) ∪ ( -1, ∞)
D)
D (-∞, ∞)
Answer
C
Graph the function. 30)
f(x) =
30)
______ A)
B)
C)
D)
Answer
C
31)
g(x) =
31)
______ A)
B)
C)
D)
Answer
A
32)
F(x) =
32)
______ A)
B)
C)
D)
Answer
C
33)
G(x) =
33)
______ A)
B)
C)
D)
Answer
D
34)
f(x) =
34)
______ A)
B)
C)
D)
Answer
A
35)
g(x) =
35)
______ A)
B)
C)
D)
Answer
B
Find a formula for the function graphed. 36)
36)
______ A)
B)
C)
D)
Answer
A
37)
37)
______ A)
f(x) =
B)
f(x) = C)
f(x) =
D)
f(x) =
Answer
D
38)
38)
______ A)
B)
C)
D)
Answer
B
39)
39)
______ A)
f(x) =
B)
f(x) = C)
f(x) =
D)
f(x) = Answer
A
40)
40)
______ A)
f(x) =
B)
f(x) = C)
f(x) =
D)
f(x) =
Answer
D
41)
41)
______ A)
f(x) =
B)
f(x) = C)
f(x) = D)
f(x) = Answer
C
42)
42)
______ A)
f(x) =
B)
f(x) = C)
f(x) =
D)
f(x) = Answer
B
43)
43)
______ A)
f(x) =
B)
f(x) =
C)
f(x) =
D)
f(x) = Answer
B
Graph the function. Determine the symmetry, if any, of the function. 44)
y =
44)
______ A)
Symmetric about the origin
B)
Symmetric about the origin
C)
No symmetry
D)
Symmetric about the y-axis
Answer
B
45)
y = -
45)
______ A)
No symmetry
B)
Symmetric about the y-axis
C)
Symmetric about the y-axis
D)
Symmetric about the y-axis
Answer
D
46)
y =
46)
______ A)
Symmetric about the origin
B)
Symmetric about the origin
C)
No symmetry
D)
Symmetric about the origin
Answer
D
47)
y = -|x|
47)
______ A)
Symmetric about the origin
B)
Symmetric about the x-axis
C)
Symmetric about the y-axis
D)
Symmetric about the y-axis
Answer
C
48)
y =
48)
______ A)
No symmetry
B)
Symmetric about the y-axis
C)
No symmetry
D)
Symmetric about the y-axis
Answer
C
49)
y = -2
49)
______ A)
No symmetry
B)
No symmetry
C)
Symmetric about the x-axis
D)
Symmetric about the x-axis
Answer
A
50)
y =
50)
______ A)
Symmetric about the y-axis
B)
No symmetry
C)
No symmetry
D)
Symmetric about the y-axis
Answer
B
51)
y =
51)
______ A)
No symmetry
B)
Symmetric about the y-axis
C)
No symmetry
D)
Symmetric about the y-axis
Answer
B
Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing.
52)
y =
52)
______ A)
Increasing -∞ < x < 0 and 0 < x < ∞
B)
Increasing -∞ < x < ∞
C)
Decreasing -∞ < x < 0;Increasing 0 < x < ∞
D)
Decreasing -∞ < x < 0 and 0 < x < ∞
Answer
D
53)
y = -
53)
______ A)
Decreasing -∞ < x < 0 Increasing 0 < x < ∞
B)
Increasing -∞ < x < 0 Decreasing 0 < x < ∞
C)
Increasing -∞ < x < 0 and 0 < x < ∞
D)
Decreasing -∞ < x < 0 and 0 < x < ∞
Answer
A
54)
y =
54)
______ A)
Decreasing -∞ < x < 0 Increasing 0 < x < ∞
B)
Increasing -∞ < x < 0 and 0 < x < ∞
C)
Decreasing -∞ < x < 0 and 0 < x < ∞
D)
Increasing -∞ < x < 0 Decreasing 0 < x < ∞
Answer
C
55)
y = -|x|
55)
______ A)
Increasing -∞ < x ≤ 0 Decreasing 0 ≤ x < ∞
B)
Increasing -∞ < x < ∞
C)
Decreasing -∞ < x < ∞
D)
Decreasing -∞ < x ≤ 0 Increasing 0 ≤ x < ∞
Answer
A
56)
y =
56)
______ A)
Decreasing -∞ < x ≤ 0
B)
Decreasing 0 ≤ x < ∞
C)
Decreasing -∞ < x ≤ 0Increasing 0 ≤ x < ∞
D)
Increasing -∞ < x ≤ 0
Answer
A
57)
y = 5
57)
______ A)
Decreasing 0 ≤ x < ∞
B)
Increasing 0 ≤ x < ∞
C)
Increasing -∞ < x < ∞
D)
Decreasing 0 ≤ x < ∞
Answer
B
58)
y =
58)
______ A)
Decreasing -∞ < x < ∞
B)
Decreasing -∞ < x ≤ 0
C)
Increasing 0 ≤ x < ∞
D)
Decreasing -∞ < x ≤ 0Increasing 0 ≤ x < ∞
Answer
B
59)
y =
59)
______ A)
Decreasing -∞ < x ≤ 0Increasing 0 ≤ x < ∞
B)
Decreasing -∞ < x < ∞
C)
Increasing -∞ < x < ∞
D)
Increasing -∞ < x < 0Decreasing 0 < x < ∞
Answer
D
Determine if the function is even, odd, or neither. 60)
f(x) = -6
60)
______ A)
Even
B)
Odd
C)
Neither Answer
A
61)
f(x) = 3x2 + 2
61)
______ A)
Even
B)
Odd
C)
Neither Answer
A
62)
f(x) = 4x4 - 6x - 5
62)
______ A)
Even
B)
Odd
C)
Neither Answer
C
63)
f(x) = 2x5 - 7x
3
63)
______ A)
Even
B)
Odd
C)
Neither Answer
B
64)
f(x) = (x - 5)(x + 8)
64)
______ A)
Even
B)
Odd
C)
Neither Answer
C
65)
f(x) =
65)
______ A)
Even
B)
Odd
C)
Neither Answer
A
66)
f(x) =
66)
______ A)
Even
B)
Odd
C)
Neither Answer
C
67)
g(x) =
67)
______ A)
Even
B)
Odd
C)
Neither Answer
B
68)
g(x) = | 5 |
68)
______ A)
Even
B)
Odd
C)
Neither Answer
A
69)
h(t) =
69)
______ A)
Even
B)
Odd
C)
Neither Answer
A
Match the equation with its graph. 70)
y =
70)
______ A)
B)
C)
D)
Answer
C
71)
y =
71)
______ A)
B)
C)
D)
Answer
D
72)
y = 5x
72)
______ A)
B)
C)
D)
Answer
B
Provide an appropriate response. 73)
Graph the functions f(x) = and g(x) = 3 + together to identify the values of x for which > 3 + .Confirm your findings algebraically. 73)
______ A)
( 8, ∞)
B)
(-∞, -2) ∪ (0, 8)
C)
( -2, 8)
D)
( -2, 0) ∪ ( 8, ∞) Answer
D
74)
Graph the functions f(x) = and g(x) = together to identify the values of x for which < .Confirm your findings algebraically. 74)
______ A)
(-∞, -3)
B)
(-1, 1) ∪ (1, ∞)
C)
(-3, -1) ∪ (1, ∞)
D)
(-3, ∞) Answer
A
Solve the problem. 75)
The variable s is proportional to t, and s = 50 when t = 150. Determine t when s = 75.
75)
______ A)
300
B)
3
C)
215
D)
225 Answer
D
76)
The kinetic energy K of a mass is proportional to the square of its velocity v. If K = 14,450 joules when what is K when v = 13 m/sec?
76)
______ A)
9295
B)
8450
C)
6760
D)
10,140 Answer
B
77)
Boyle's Law says that volume V of a gas at constant temperature increases whenever the pressure P decreases, so that V
and P are inversely proportional. If P = 14.1 lbs/ when V = 900 , then what is V when P = 21 lbs/ ?
77)
______ A)
B)
C)
D)
Answer
B
78)
A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 inches by 29 inches by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a function of x.
78)
______ A)
V(x) = x( 12 - x)( 29 - x)
B)
V(x) = ( 12 - x)( 29 - x) C)
V(x) = x( 12 - 2x)( 29 - 2x)
D)
V(x) = ( 12 - 2x)( 29 - 2x) Answer
C
79)
The figure shown here shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 8 units long. Express the area A of the rectangle in terms of x.
79)
______ A)
A(x) = 2x( 4 - x)
B)
A(x) = 2x(x - 4)
C)
A(x) = 2
D)
A(x) = x( 4 - x) Answer
A
80)
A power plant is located on a river that is 600 feet wide. To lay a new cable from the plant to a location in a city 2 miles downstream on the opposite side costs $ 225 per foot across the river and $ 150 per foot along the land. Suppose that the cable goes from the plant to a point Q on the opposite side that is x feet from the point P directly opposite the plant. Write a function C(x) that gives the cost of laying the cable in terms of the
80)
______ A)
C(x) = 225( 600 - x) + 150( 2 - x)
B)
C(x) = 150 + 225( 10,560 - x) C)
C(x) = 225 + 150( 2 - x)
D)
C(x) = 225 + 150( 10,560 - x) Answer
D
Provide an appropriate response. 81)
Consider the function y = . Can x be negative?
81)
______ A)
Yes
B)
No Answer
A
82)
Consider the function y = . Can x be greater than 0, but less than 1?
82)
______ A)
Yes
B)
No Answer
B
83)
What is the domain of the function y = ?
83)
______ A)
(-∞, ∞)
B)
(0, 1]
C)
(-∞, 0) ∪ [1, ∞)
D)
(-∞, 0) ∪ (1, ∞) Answer
C
84)
Graph the equation = x and decide whether or not the graph represents a function of x.
84)
______ A)
Function
B)
Not a Function Answer
B
85)
Graph the equation |x + y| = 1 and decide whether or not the graph represents a function of x.
85)
______ A)
Function
B)
Not a Function Answer
B
86)
For what values of x is = 3?
86)
______ A)
2 ≤ x < 3
B)
2 < x ≤ 3
C)
3 < x ≤ 4
D)
3 ≤ x < 4 Answer
D
87)
For what values of x is = -1?
87)
______ A)
-1 ≤ x < 0
B)
-2 < x ≤ -1
C)
-2 ≤ x < -1
D)
-1 < x ≤ 0 Answer
B
88)
What real numbers x satisfy the equation = ?
88)
______ A)
{x|x ∈ integers}
B)
{x|x = 0} C)
{x|x ∈ real numbers}
D)
∅Answer
A
89)
Graph the function f(x) = .
89)
______ A)
B)
C)
D)
Answer
D
90)
Graph the function f(x) = .
90)
______ A)
B)
C)
D)
Answer
C
Find the domain and range for the indicated function. 91)
f(x) = , g(x) = ; f - g
91)
______ A)
D x ≥ -11
R y ≥ B)
D x ≥ 11R y ≥ 0 C)
D x ≥ 11
R y ≥ D)
D x ≥ -11R y ≥ 0
Answer
C
92)
f(x) = , g(x) = ; g - f
92)
______ A)
D x ≥ 13
R y ≥ - B)
D x ≥ -13
R y ≥ - C)
D x ≥ 13R y ≥ 0 D)
D x ≥ 13
R y ≥ Answer
A
93)
f(x) = , g(x) = ; f ∙ g
93)
______ A)
D x ≥ 10R y > 0 B)
D x > 10R y ≥ 0 C)
D x ≥ 10R y ≥ 0 D)
D x ≥ 10R -∞ < y < ∞
Answer
C
94)
f(x) = 8, g(x) = 8 + ; f/g
94)
______ A)
D x ≥ 0R y ≤ 8 B)
D x ≥ -8R y ≥ 0 C)
D x ≥ 0R y ≤ 1 D)
D x ≥ 0R y ≥ 1
Answer
C
95)
f(x) = 7, g(x) = 7 + ; g/f
95)
______ A)
D x ≥ -7R y ≥ 0 B)
D x ≥ 0R y ≤ 7 C)
D x ≥ 0R y ≤ 1 D)
D x ≥ 0R y ≥ 1
Answer
D
Solve the problem. 96)
If f(x) = 3x + 8 and g(x) = 3x - 1, find f(g(x)).
96)
______ A)
9x + 5
B)
9x + 23
C)
9x + 7
D)
9x + 11 Answer
A
97)
If f(x) = -2x + 3 and g(x) = 5x + 5, find g(f(x)).
97)
______ A)
-10x + 13
B)
-10x + 20
C)
10x + 20
D)
-10x - 10 Answer
B
98)
If f(x) = and g(x) = 9x + 4, find g(f(x)).
98)
______ A)
x + 8
B)
-
C)
9x + 32
D)
x Answer
D
99)
If f(x) = and g(x) = 8x - 9, find f(g(x)).
99)
______ A)
2
B)
2
C)
8
D)
8 - 9 Answer
B
100)
If f(x) = 4x2 + 6x + 8 and g(x) = 6x - 7, find g(f(x)).
100)
_____ A)
4x2 + 6x + 1
B)
24x2 + 36x + 55
C)
24x2 + 36x + 41
D)
4x2 + 36x + 41
Answer
C
101)
If f(x) = and g(x) = 7x6, find g(f(x)).
101)
_____ A)
B)
C)
D)
Answer
D
102)
If f(x) = 4x + 7 and g(x) = -7x2 + 5x + 2, find g(f(4)).
102)
_____ A)
-3586
B)
-17
C)
-44
D)
-353 Answer
A
103)
If f(x) = -2x - 9 and g(x) = -4x2 - 7x + 1, find g(f( -2)).
103)
_____ A)
-64
B)
-7
C)
-55
D)
56 Answer
A
104)
If f(x) = , g(x) = , and h(x) = 3x+ 9, find f(g(h(x))).
104)
_____ A)
3 + 9
B)
C)
+ 3
D)
Answer
B
105)
If f(x) = , g(x) = , and h(x) = 5x+ 10, find h(g(f(x))).
105)
_____ A)
+ 10
B)
C)
5 + 10
D)
+ 2 Answer
A
Express the given function as a composite of functions f and g such that y = f(g(x)). 106)
y =
106)
_____ A)
f(x) = , g(x) = -
B)
f(x) = , g(x) = - 7 C)
f(x) = , g(x) = - 7
D)
f(x) = , g(x) = x - 7 Answer
B
107)
y =
107)
_____ A)
f(x) = , g(x) = 4x + 10
B)
f(x) = , g(x) = 4x - 10 C)
f(x) = - , g(x) = 4x + 10
D)
f(x) = x, g(x) = 4x + 10 Answer
A
108)
y = + 8
108)
_____ A)
f(x) = , g(x) = + 8
B)
f(x) = x + 8, g(x) = C)
f(x) = x, g(x) = + 8
D)
f(x) = , g(x) = 8 Answer
B
109)
y =
109)
_____ A)
f(x) = 6, g(x) =
B)
f(x) = , g(x) = 6 C)
f(x) = , g(x) = 7x + 6
D)
f(x) = , g(x) = 7x + 6 Answer
C
110)
y =
110)
_____ A)
f(x) = 8x - 19, g(x) =
B)
f(x) = 8 , g(x) = x - 19 C)
f(x) = ( 8 , g(x) = -19
D)
f(x) = , g(x) = 8x - 19 Answer
D
Solve the problem. 111)
Let f(x) = . Find a function y = g(x) so that (f ∘ g)(x) = x.
111)
_____ A)
g(x) =
B)
g(x) = x(x - 4)
C)
g(x) =
D)
g(x) = Answer
D
112)
Let f(x) = . Find a function y = g(x) so that (f ∘ g)(x) = .
112)
_____ A)
g(x) = + 5
B)
g(x) =
C)
g(x) = - 5
D)
g(x) = 2x Answer
B
113)
Let g(x) = . Find a function y = f(x) so that (f ∘ g)(x) = .
113)
_____ A)
f(x) =
B)
f(x) = x
C)
f(x) =
D)
f(x) = Answer
A
114)
Let g(x) = x + 8. Find a function y = f(x) so that (f ∘ g)(x) = 3x + 24
114)
_____ A)
f(x) = 3x
B)
f(x) = 3x - 8
C)
f(x) = 3x + 8
D)
f(x) = 3(x + 1) Answer
A
115)
The accompanying figure shows the graph of y = shifted to a new position. Write the equation for the new graph.
115)
_____ A)
y =
B)
y = x2 + 5
C)
y =
D)
y = x2 - 5
Answer
D
116)
The accompanying figure shows the graph of y = shifted to a new position. Write the equation for the new graph.
116)
_____ A)
y =
B)
y =
C)
y = x2 + 5
D)
y = x2 - 5
Answer
C
117)
The accompanying figure shows the graph of y = shifted to a new position. Write the equation for the new graph.
117)
_____ A)
y =
B)
y = x2 - 4
C)
y = x2 + 4
D)
y = Answer
D
118)
The accompanying figure shows the graph of y = shifted to a new position. Write the equation for the new graph.
118)
_____ A)
y = x2 + 6
B)
y =
C)
y = x2 - 6
D)
y = Answer
D
119)
The accompanying figure shows the graph of y = - shifted to a new position. Write the equation for the new graph.
119)
_____ A)
y = -x2
- 6
B)
y = -
C)
y = -x2
+ 6
D)
y = - Answer
A
120)
The accompanying figure shows the graph of y = - shifted to a new position. Write the equation for the new graph.
120)
_____ A)
y = -
B)
y = -
C)
y = -x2
+ 5
D)
y = -x2
- 5 Answer
C
121)
The accompanying figure shows the graph of y = - shifted to a new position. Write the equation for the new graph.
121)
_____ A)
y = -x2
- 3
B)
y = -
C)
y = -
D)
y = -x2
+ 3 Answer
B
122)
The accompanying figure shows the graph of y = - shifted to a new position. Write the equation for the new graph.
122)
_____ A)
y = -
B)
y = -
C)
y = -x2
- 2
D)
y = -x2
+ 2 Answer
B
123)
The accompanying figure shows the graph of y = shifted to a new position. Write the equation for the new graph.
123)
_____ A)
y = (x - 1)2 + 2
B)
y = (x + 1)2 + 2
C)
y = (x - 2)2 + 1
D)
y = (x + 1)2 - 2
Answer
B
124)
The accompanying figure shows the graph of y = - shifted to a new position. Write the equation for the new graph.
124)
_____ A)
y = -(x - 3)2 - 2
B)
y = -(x + 3)2 + 2
C)
y = -(x - 2)2 - 3
D)
y = -(x + 3)2 - 2
Answer
D
The problem tells how many units and in what direction the graph of the given equation is to be shifted. Give an equation for the shifted graph. Then sketch the original graph with a dashed line and the shifted graph with a solid line.
125)
+ = 9 Up 4, right 4
125)
_____ A)
(x - 4)2
+ (y + 4)2 = 9
B)
(x - 4)2
+ (y - 4)2 = 9
C)
(x + 4)2 + (y + 4)
2 = 9
D)
(x + 4)2 + (y - 4)
2 = 9
Answer
B
126)
y = Down 1, left 1
126)
_____ A)
y + 1 =
B)
y - 1 =
C)
y + 1 =
D)
y - 1 =
Answer
A
127)
y = - Left 5
127)
_____ A)
y =
B)
y = - 5
C)
y =
D)
y = + 5
Answer
C
128)
y = Down 5, right 3
128)
_____ A)
y + 5 =
B)
y - 5 =
C)
y - 5 =
D)
y + 5 =
Answer
A
Graph the function. 129)
y = + 2
129)
_____ A)
B)
C)
D)
Answer
D
130)
y = |x - 2| + 7
130)
_____ A)
B)
C)
D)
Answer
B
131)
y = 3 -
131)
_____ A)
B)
C)
D)
Answer
C
132)
y =
132)
_____ A)
B)
C)
D)
Answer
C
133)
y - 1 =
133)
_____ A)
B)
C)
D)
Answer
A
134)
y =
134)
_____ A)
B)
C)
D)
Answer
A
135)
y = - 4
135)
_____ A)
B)
C)
D)
Answer
A
136)
y = - 4
136)
_____ A)
B)
C)
D)
Answer
C
137)
y =
137)
_____ A)
B)
C)
D)
Answer
B
138)
y =
138)
_____ A)
B)
C)
D)
Answer
B
139)
y = + 3
139)
_____ A)
B)
C)
D)
Answer
A
140)
y = - 3
140)
_____ A)
B)
C)
D)
Answer
A
141)
y = + 2
141)
_____ A)
B)
C)
D)
Answer
C
142)
y = - 3
142)
_____ A)
B)
C)
D)
Answer
B
143)
y =
143)
_____ A)
B)
C)
D)
Answer
B
144)
y = - 4
144)
_____ A)
B)
C)
D)
Answer
A
Using the graph below, find the domain and range of the given function, and sketch the graph.
145)
y = -f(x)
145)
_____ A)
D [-4, 5]; R [-3, 3]
B)
D [-5, 4]; R [-3, 3]
C)
D [-7.5, 1]; R [-1, 5]
D)
D [-7, 2]; R [-4, 2]
Answer
B
146)
y = f(-x)
146)
_____ A)
D [-4, 5]; R [-3, 4]
B)
D [-4, 5]; R [-3, 3]
C)
D [-5, 4]; R [-3, 3]
D)
D [-4, 5]; R [-3, 3]
Answer
D
147)
y = f(x + 2) -1
147)
_____ A)
D [-5, 4]; R [-3, 3]
B)
D [-4, 5]; R [-3, 3]
C)
D [-8, 1]; R [-2.5, 5]
D)
D [-7, 2]; R [-4, 2]
Answer
D
148)
y = f(-x - 2) + 1
148)
_____ A)
D [-6, 3]; R [-2, 4]
B)
D [-7, 2]; R [-2, 4]
C)
D [-3, 6]; R [-2, 4]
D)
D [-7, 2]; R [-2, 4]
Answer
A
The problem tells by what factor and direction the graph of the given function is to be stretched or compressed. Give an equation for the stretched or compressed graph.
149)
y = + 4 stretched horizontally by a factor of 3
149)
_____ A)
y = 3 + 12
B)
y = + 4
C)
y = 9 + 4
D)
y = + 4 Answer
B
150)
y = - 2 compressed vertically by a factor of 5
150)
_____ A)
y = -
B)
y = 5 - 10
C)
y = 25 - 2
D)
y = - 2 Answer
A
151)
y = 1 + stretched vertically by a factor of 3
151)
_____ A)
y = 3 +
B)
y = 1 +
C)
y = 1 +
D)
y = + Answer
A
152)
y = 1 + compressed horizontally by a factor of 9
152)
_____ A)
y = +
B)
y = 1 +
C)
y = 9 +
D)
y = 1 + Answer
B
153)
y = compressed vertically by a factor of 3
153)
_____ A)
y =
B)
y =
C)
y =
D)
y = 3 Answer
A
154)
y = + 1 stretched vertically by a factor of 3
154)
_____ A)
y = +
B)
y = 3 + 1
C)
y = 27 + 1
D)
y = 3 + 3 Answer
D
The equation of an ellipse is given. Put the equation in standard form and sketch the ellipse. 155)
16 + 64 = 1024
155)
_____ A)
+ = 1
B)
+ = 1
C)
+ = 1
D)
+ = 1
Answer
B
156)
64 + 4 = 256
156)
_____ A)
+ = 1
B)
+ = 1
C)
+ = 1
D)
+ = 1
Answer
D
157)
3 + = 3
157)
_____ A)
+ = 1
B)
+ = 1
C)
+ = 1
D)
+ = 1
Answer
C
158)
+ 6 = 6
158)
_____ A)
+ = 1
B)
+ = 1
C)
+ = 1
D)
+ = 1
Answer
C
159)
16 + 4 = 64
159)
_____ A)
+ = 1
B)
+ = 1
C)
+ = 1
D)
+ = 1
Answer
C
Assume that f is an even function, g is an odd function, and both f and g are defined on the entire real line. State whether the combination of functions (where defined) is even or odd.
160)
f g
160)
_____ A)
Even
B)
Odd Answer
B
161)
f/ g
161)
_____ A)
Even
B)
Odd Answer
B
162)
162)
_____ A)
Even
B)
Odd Answer
A
163)
g ∘ f
163)
_____ A)
Even
B)
Odd Answer
A
164)
f ∘ f
164)
_____ A)
Even
B)
Odd Answer
A
165)
g ∘ g
165)
_____ A)
Even
B)
Odd Answer
B
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem.
166)
Graph the functions f(x) = and g(x) = together with their sum, product, two differences, and two quotients.
166)
____________ Answer
167)
Let f(x) = x - 6 and g(x) = . Graph f and g together with f ∘ g and g ∘ f.
167)
____________ Answer
1)
D 2)
A 3)
C 4)
D 5)
D 6)
A 7)
A 8)
D 9)
C 10)
A 11)
A 12)
B 13)
B 14)
A 15)
A 16)
C 17)
B 18)
C 19)
A 20)
A 21)
C 22)
D 23)
C 24)
B 25)
A 26)
D 27)
B 28)
B 29)
C 30)
C 31)
A 32)
C 33)
D 34)
A 35)
B 36)
A 37)
D 38)
B 39)
A 40)
D 41)
C 42)
B 43)
B 44)
B 45)
D 46)
D 47)
C 48)
C 49)
A 50)
B 51)
B 52)
D 53)
A 54)
C 55)
A 56)
A 57)
B 58)
B 59)
D 60)
A 61)
A 62)
C 63)
B 64)
C 65)
A 66)
C 67)
B 68)
A 69)
A 70)
C 71)
D 72)
B 73)
D 74)
A 75)
D 76)
B 77)
B 78)
C 79)
A 80)
D 81)
A 82)
B 83)
C 84)
B 85)
B 86)
D 87)
B 88)
A 89)
D 90)
C 91)
C 92)
A 93)
C 94)
C 95)
D 96)
A 97)
B 98)
D 99)
B 100)
C 101)
D 102)
A 103)
A 104)
B 105)
A 106)
B 107)
A 108)
B 109)
C 110)
D 111)
D 112)
B 113)
A 114)
A 115)
D 116)
C 117)
D 118)
D 119)
A 120)
C 121)
B 122)
B 123)
B 124)
D 125)
B 126)
A 127)
C 128)
A 129)
D 130)
B 131)
C 132)
C 133)
A 134)
A 135)
A 136)
C 137)
B 138)
B 139)
A 140)
A 141)
C 142)
B 143)
B 144)
A 145)
B 146)
D 147)
D 148)
A 149)
B 150)
A 151)
A 152)
B 153)
A 154)
D 155)
B 156)
D 157)
C 158)
C 159)
C 160)
B 161)
B 162)
A 163)
A 164)
A 165)
B 166)
167)
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