41)
f(x) =9x2–x4
41)
A)
B)
C)
D)
42)
h(x) =–5x + 6
4x + 6
42)
A)
y =1
B)
y = – 5
4
C)
y = – 5
D)
no horizontal asymptote
43)
g(x) =x
x – 1
43)
A)
x = 0 and x = – 1
B)
x =1
C)
x = 0 and x =1
D)
no vertical asymptote
44)
3x4+ 17x3+ 61x2+ 73x + 26 = 0
44)
A)
1, –2
3, –3±2i
B)
–1, –2
3, –3±2i
C)
–1, –2
3, –2±3i
D)
1, –2
3, –2±3i
45)
f(x) =(2x – 1)3(x3+ 3)(x + 5)
45)
A)
14
B)
3
C)
7
D)
6
46)
f(x) = – 5x5+ x3
46)
A)
Even
B)
Neither
C)
Odd
47)
f(x) =4x2
x2– 25
47)
A)
B)
C)
D)
48)
A box with an open top is formed by cutting squares out of the corners of a rectangular piece of
cardboard and then folding up the sides. If x represents the length of the side of the square cut from
each corner, and if the original piece of cardboard is 19 inches by 16 inches, what size square must
be cut if the volume of the box is to be 352 cubic inches?
48)
A)
8 in. by 8 in. square
B)
11 in. by 11 in. square
C)
1 in. by 1 in. square
D)
4 in. by 4 in. square
49)
A company that produces bicycles has costs given by the function C(x) =25x + 25,000, where x is
the number of bicycles manufactured and C(x) is measured in dollars. The average cost to
manufacture each bicycle is given by
_
C(x) =25x + 25,000
x.
What is the horizontal asymptote for the function
_
C? Describe what this means in practical terms.
49)
A)
y =25,000; 25,000 is the maximum number of bicycles the company can produce.
B)
y =25; 25 is the minimum number of bicycles the company can produce.
C)
y =25,000; $25,000 is the least possible cost for running the company.
D)
y = $25; The cost of producing each bicycle approaches $25 as production increases.
50)
f(x) =x2+ 7x + 12
x2– 1
50)
A)
B)
C)
D)
51)
51)
A)
not a polynomial function
B)
could be a polynomial function
52)
f(x) = 6x4+3x3–4x2+ 2
52)
A)
±1
6, ±1
3, ±1
2, ± 1, ± 2
B)
±1
6, ±1
3, ±1
2, ±2
3, ± 1, ± 2
C)
±1
6, ±1
3, ±1
2, ±2
3, ± 1, ± 2, ± 3
D)
±1
2, ±3
2, ± 1, ± 2, ± 3, ± 6
53)
f(x) =x2(5 –x2)
53)
A)
Odd
B)
Even
C)
Neither
54)
f(x) =1
3x2+9x4
54)
A)
Neither
B)
Even
C)
Odd
55)
A drug is injected into a patient and the concentration of the drug is monitored. The drug‘s
concentration, C(t), in milligrams per liter after t hours is modeled by
C(t) =8t
2t2+1.
Estimate the drug’s concentration after 3 hours. (Round to the nearest hundredth.)
55)
A)
3.49 milligrams per liter
B)
1.26 milligrams per liter
C)
1.32 milligrams per liter
D)
3.43 milligrams per liter
56)
x3+ 2x2+ 5x – 26 = 0
56)
A)
{2, –2±3i}
B)
{2, 3±5}
C)
{–2, –2+5, –4–5}
D)
{2, 3±2i}
A
57)
57)
A)
Even
B)
Odd
C)
Neither
B
B
58)
f(x) = – 9x9–5x8–10x7+8x6+ x +10
58)
A)
1 positive zero, 3 or 1 negative zeros
B)
1 positive zero, 2 or 0 negative zeros
C)
1 positive zero, 4 or 2 negative zeros
D)
1 positive zero, 4, 2 or 0 negative zeros
59)
Determine whether f(x) =x4–x2 is even, odd, or neither. Use your answer to explain why the
graph in the figure shown cannot be the graph of f.
59)
A)
The function is even. The graph of f should have y–axis symmetry, but the graph in the figure
has origin symmetry.
B)
The function is neither even nor odd. The graph in the figure has origin symmetry.
C)
The function is odd. The graph of f should have y–axis symmetry, but the graph in the figure
has origin symmetry.
D)
The function is even. The graph of f should have origin symmetry, but the graph in the figure
has y–axis symmetry.
60)
f(x) =x3+ 6x2+9x
60)
A)
1 with multiplicity 1, crosses x–axis; –3 with multiplicity 2, touches x–axis and turns
B)
0 with multiplicity 1, touches x–axis and turns; –3 with multiplicity 2, crosses x–axis
C)
0 with multiplicity 1, crosses x–axis; 3 with multiplicity 2, touches x–axis and turns
D)
0 with multiplicity 1, crosses x–axis; –3 with multiplicity 2, touches x–axis and turns
61)
Use the Rational Zero Theorem to list all possible rational zeros of f(x) = – 2x3+2x2–3x + 8.
61)
A)
±1
4, ±1
2, ±1, ±2, ±4, ±8
B)
±1
2, ±1, ±2, ±4
C)
±1
2, ±1, ±2, ±4, ±8
D)
±1
8,±1
4, ±1
2, ±1, ±2, ±4, ±8
62)
f(x) =6x2
x2+36
62)
A)
no vertical asymptote; y = 1
B)
no vertical asymptote; y = 1
C)
no vertical asymptote; y =6
D)
x = – 6, x =6; y =6
63)
g(x) =x – 1
x(x + 1)
63)
A)
x = – 1
B)
x =1 and x = – 1
C)
x = 0 and x = – 1
D)
no vertical asymptote
64)
f(x) =4(x + 4)(x – 7)2
64)
A)
–4 with multiplicity 1, touches x–axis and turns; 7 with multiplicity 2, crosses x–axis
B)
–4 with multiplicity 1, crosses x–axis; 7 with multiplicity 2, touches x–axis and turns
C)
4 with multiplicity 1, crosses x–axis; –7 with multiplicity 2, touches x–axis and turns
D)
4 with multiplicity 1, touches x–axis and turns; –7 with multiplicity 2, crosses x–axis
65)
f(x) = – 3
x2– 1
65)
A)
B)
C)
D)
66)
66)
A)
could be a polynomial function
B)
not a polynomial function
67)
f(x) = – x2– 4x + 3
67)
A)
2
B)
1
C)
0
D)
3
68)
68)
A)
Odd
B)
Neither
C)
Even
69)
f(x) = x(5–x2)
69)
A)
Neither
B)
Odd
C)
Even
70)
Solve the equation 2x3– 9x2+ 7x + 6 = 0 given that 2 is a zero of f(x) =2x3– 9x2+ 7x + 6.
70)
A)
–1
2, –1, 2
B)
1
2, 2, –3
C)
–1
2, 2, 3
D)
1
2, –1, 2
71)
f(x) =x5+7x6
71)
A)
1
B)
7
C)
5
D)
6
72)
Solve the equation 3x3– 19x2+ 30x – 8 = 0 given that 4 is a zero of f(x) =3x3– 19x2+ 30x – 8.
72)
A)
–4
3, 1, 4
B)
4
3, 1, 4
C)
–1
3, 2, 4
D)
1
3, 2, 4
73)
h(x) =x
x(x + 5)
73)
A)
x = 0 and x =5
B)
x = – 5
C)
x = 0 and x = – 5
D)
no vertical asymptote
74)
f(x) =4x
2x2+ 1
74)
A)
y =2
B)
y =1
2
C)
y = 0
D)
no horizontal asymptote
75)
The graph displays the percentage of professional works completed in each age decade of life by
556 people who lived to be at least 79. Describe the degree and the leading coefficient of the
function that can used to model the data in the graph.
75)
A)
degree: even; leading coefficient: negative
B)
degree: odd; leading coefficient: negative
C)
degree: odd; leading coefficient: positive
D)
degree: even; leading coefficient: positive
76)
76)
A)
could be a polynomial function
B)
not a polynomial function
77)
f(x) = – 4x4+ 4x3+ 5x2+ 5x + 5
77)
A)
falls to the left and rises to the right
B)
falls to the left and to the right
C)
rises to the left and to the right
D)
rises to the left and falls to the right
78)
78)
A)
could be a polynomial function
B)
not a polynomial function
79)
f(x) =2x3– 11x2+ 17x – 6
79)
A)
3
2, 1, and 2
B)
–3
2, 1, and –2
C)
1
2, 2, and 3
D)
–1
2, 2, and –3
80)
f(x) =3x –3
2(x + 4)3
80)
A)
3
2 with multiplicity 1, touches the x–axis and turns; –4 with multiplicity 3, touches x–axis
and turns
B)
–3
2 with multiplicity 1, touches the x–axis and turns; 4 with multiplicity 3, touches x–axis
and turns
C)
–3
2 with multiplicity 1, crosses x–axis; 4 with multiplicity 3, crosses x–axis
D)
3
2 with multiplicity 1, crosses x–axis; –4 with multiplicity 3, crosses x–axis
81)
f(x) = – 2x3+3x2–4x + 8
81)
A)
±1
4, ±1
2, ± 1, ± 2, ± 4, ± 8
B)
±1
8,±1
4, ±1
2, ± 1, ± 2, ± 4, ± 8
C)
±1
2, ± 1, ± 2, ± 4, ± 8
D)
±1
2, ± 1, ± 2, ± 4
82)
3x3– 19x2+ 30x – 8 = 0
82)
A)
4
3, 1, 2
B)
1
3, 2, 4
C)
–4
3, 1, –2
D)
–1
3, 2, –4
83)
83)
A)
Neither
B)
Even
C)
Odd
84)
f(x) =6x7–3x2+ x +8
84)
A)
2 or 0 positive zeros, 1 or 0 negative zeros
B)
2 or 0 positive zeros, 2 or 0 negative zeros
C)
2 or 0 positive zeros, 1 negative zero
D)
3 or 1 positive zeros, 3 or 1 negative zeros
85)
f(x) =x2– 1
x2–9
85)
A)
x = – 3, x =3; y = 1
B)
no vertical asymptote; y = 1
C)
x = – 3, x =3; y = 1
D)
x = – 3, x =3; y = 0
86)
f(x) =x2+ 2x – 15
(x – 5)2
86)
A)
B)
C)
D)
87)
f(x) =x5(x5+ 4)(7x – 4)
87)
A)
10
B)
70
C)
5
D)
11
88)
f(x) =x4– 9x2
88)
A)
B)
C)
D)