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C)
D)
Use the Factor Theorem to solve the equation.
89)
Solve the equation x3+ 3x2- 4x - 12 = 0 given that 2 is a zero of f(x) =x3+ 3x2- 4x - 12.
89)
A)
{-3, -2, 2}
B)
{-2, 2}
C)
{-3, 2}
D)
{-2, 2, 3}
Find the vertical asymptotes, if any, of the graph of the rational function.
90)
r(x) =x -6
x2- 36
90)
A)
x =6
B)
x =6, x = - 6
C)
x = - 6
D)
no vertical asymptote
Determine whether the function is even, odd, or neither.
91)
f(x) =3x2+ x4
91)
A)
Even
B)
Neither
C)
Odd
Use the Rational Zero Theorem to list all possible rational zeros for the given function.
92)
f(x) =x3-7x2+3x -21
92)
A)
± 1, ±7, ±3, ±21
B)
± 1, ±7, ±3
C)
± 1, ±1
7, ±1
3, ±1
21
D)
± 1, ±1
7, ±1
3, ±1
21 , ±7, ±3, ±21
41
Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the
x-axis, or touches the x-axis and turns around, at each zero.
93)
f(x) =x +1
5
4(x + 2)5
93)
A)
1
5 with multiplicity 4, crosses x-axis; 2 with multiplicity 5, touches x-axis and turns
B)
1
5 with multiplicity 4, touches x-axis and turns; 2 with multiplicity 5, crosses x-axis
C)
-1
5 with multiplicity 4, touches x-axis and turns; -2 with multiplicity 5, crosses x-axis
D)
-1
5 with multiplicity 4, crosses x-axis; -2 with multiplicity 5, touches x-axis and turns
Solve.
94)
Suppose that a polynomial function is used to model the data shown in the graph below.
For what intervals is the function decreasing?
94)
A)
10 through 30
B)
10 through 20 and 30 through 50
C)
0 through 30
D)
0 through 10 and 30 through 50
Use the Rational Zero Theorem to list all possible rational zeros for the given function.
95)
f(x) = - 4x4+2x2-3x + 6
95)
A)
±1
6, ±1
2, ±1
3, ±2
3, ±4
3, ± 1, ± 2, ± 4
B)
±1
4, ±1
2, ±2
3, ±3
4, ±3
2, ± 1, ± 2, ± 3, ± 6
C)
±1
4, ±1
2, ±3
4, ±3
2, ± 1, ± 2, ± 3, ± 4, ± 6
D)
±1
4, ±1
2, ±3
4, ±3
2, ± 1, ± 2, ± 3, ± 6
96)
f(x) =x5-6x2+5x +15
96)
A)
± 1, ±1
5, ±1
3, ±1
15
B)
± 1, ±5, ±3
C)
± 1, ±1
5, ±1
3, ±1
15 , ±5, ±3, ±15
D)
± 1, ±5, ±3, ±15
43
Solve the problem.
97)
Consider the function whose equation is given by f(x) =3x4+x3-17x2-5x +10.
a. List all possible rational zeros.
b. Use the graph of f in the figure shown and synthetic division to find all zeros of the function.
97)
A)
a. ±1, ±2, ±5, ±10, ±1
3, ±2
3, ±5
3, ±10
3
b. -5, -1, 2
3, 5
B)
a. ±1, ±2, ±5, ±10, ±1
3, ±2
3, ±5
3, ±10
3
b. -5, -1, -2
3, 5
C)
a. ±1, ±2, ±5, ±10
b. -5, -1, 2
3, 5
D)
a. ±1, ±2, ±5, ±10, ±1
3, ±2
3, ±5
3, ±10
3
b. -5, -1, 2
3, 5
Use the Rational Zero Theorem to list all possible rational zeros for the given function.
98)
f(x) =5x5-5x2+5x - 1
98)
A)
±5, ±1
5
B)
± 1, ±1
5
C)
± 1, ±5, ±1
5
D)
± 1, ±5
44
Solve.
99)
Suppose that a polynomial function is used to model the data shown in the graph below.
For what intervals is the function increasing?
99)
A)
0 through 10 and 30 through 50
B)
0 through 10 and 40 through 50
C)
0 through 20 and 30 through 50
D)
0 through 50
Graph the rational function.
100)
f(x) =3x2
x2+ 36
100)
A)
B)
45
C)
D)
Solve the problem.
101)
The graph displays the percentage of professional works completed in each age decade of life by
556 scientists who lived to be at least 79. Use the graph to solve the polynomial equation f(x) =24.
Describe what this means in terms of an age decade and productivity.
101)
A)
60s; Scientists completed 24% of their professional works in their 60s.
B)
70s; Scientists completed 24% of their professional works in their 70s.
C)
40s; Scientists completed 24% of their professional works in their 40s.
D)
50s; Scientists completed 24% of their professional works in their 50s.
Graph the rational function.
46
102)
f(x) =2x
x2- 9
102)
A)
B)
C)
D)
103)
f(x) =x - 2
x2- x - 42
103)
A)
B)
C)
D)
Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function.
104)
f(x) =3x3- 2x2+ 2x + 5
104)
A)
rises to the left and falls to the right
B)
rises to the left and to the right
C)
falls to the left and to the right
D)
falls to the left and rises to the right
105)
f(x) = - 5x3- 5x2- 4x - 2
105)
A)
rises to the left and to the right
B)
falls to the left and rises to the right
C)
falls to the left and to the right
D)
rises to the left and falls to the right
Find the horizontal asymptote, if any, of the graph of the rational function.
106)
g(x) =2x2- 4x - 9
8x2- 3x + 5
106)
A)
y = 0
B)
y =1
4
C)
y =4
3
D)
no horizontal asymptote
Determine the maximum possible number of turning points for the graph of the function.
107)
f(x) = (x - 7)(x - 1)(x + 6)(x - 5)
107)
A)
3
B)
4
C)
1
D)
0
49
Solve the problem.
108)
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.
Find
_
C (100). (Round to the nearest dollar, if necessary.)
108)
A)
$295
B)
$275
C)
$48
D)
$50
Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function.
109)
f(x) =5x4- 2x3- 5x2- 4x - 2
109)
A)
rises to the left and falls to the right
B)
falls to the left and rises to the right
C)
falls to the left and to the right
D)
rises to the left and to the right
Graph the function.
110)
f(x) =7x -x3-x5
110)
A)
B)
50
C)
D)
Solve the equation.
111)
x4- 6x3+ 7x2- 6x + 6 = 0
111)
A)
{±i, 3±3}
B)
{±i, 1 ±3}
C)
{±i, -3±3}
D)
{±i, 3± 2 3}
Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function.
112)
f(x) =x7+x4+x2+ x +3
112)
A)
no positive zeros, 2 or 0 negative zeros
B)
no positive zeros, 3 or 1 negative zeros
C)
no positive zeros, 1 negative zero
D)
no positive zeros, no negative zeros
Find the zeros of the polynomial function by factoring.
113)
f(x) =x3+ 2x2- 9x - 18
113)
A)
-2 and 9
B)
-2, -3, and 3
C)
-3 and 3
D)
2, -3, and 3
51
Find the vertical asymptotes, if any, of the graph of the rational function.
114)
f(x) =x
x2+ 8
114)
A)
x =8
B)
x = - 8
C)
x = - 8, x =8
D)
no vertical asymptote
Determine whether the function is even, odd, or neither.
115)
f(x) =6x5+8x7
115)
A)
Neither
B)
Odd
C)
Even
Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function.
116)
f(x) =10x6- 8x5+x4-12x3+16
116)
A)
4 positive zeros, no negative zeros
B)
4, 2 or 0 positive zeros, no negative zeros
C)
4 or 2 positive zeros, no negative zeros
D)
4, 2 or 0 positive zeros, 1 negative zero
52
