CHAPTER 2 RevIEw
precalculus
y = (x+2)2
y = (x-2)2 -1
y = -(x+1)2 + 3
4)
The number of horsepower H required to overcome wind drag on a certain car is approximated by
H(s) = 0.002s2 + 0.05s - 0.029 , 0 < s < 100 where s is the speed of the car in miles per hour.
a) Use a graphing calculator to graph.
b) Estimate the maximum speed of the car if the power required to overcome wind drag is not to exceed 10
horsepower. Round your answer to the nearest tenth.
4)
The number of horsepower H required to overcome wind drag on a certain car is approximated by
H(s) = 0.002s2 + 0.05s - 0.029 , 0 < s < 100 where s is the speed of the car in miles per hour.
a) Use a graphing calculator to graph.
b) Estimate the maximum speed of the car if the power required to overcome wind drag is not to exceed 10
horsepower. Round your answer to the nearest tenth.
4)
The number of horsepower H required to overcome wind drag on a certain car is approximated by
H(s) = 0.002s2 + 0.05s - 0.029 , 0 < s < 100 where s is the speed of the car in miles per hour.
a) Use a graphing calculator to graph.
b) Estimate the maximum speed of the car if the power required to overcome wind drag is not to exceed 10
horsepower. Round your answer to the nearest tenth.
4)
The number of horsepower H required to overcome wind drag on a certain car is approximated by
H(s) = 0.002s2 + 0.05s - 0.029 , 0 < s < 100 where s is the speed of the car in miles per hour.
a) Use a graphing calculator to graph.
b) Estimate the maximum speed of the car if the power required to overcome wind drag is not to exceed 10
horsepower. Round your answer to the nearest tenth.
59.4 MPH
5) f(x) =
2
x
- 16
2
x
5) f(x) = - 16
= (x )(x
)
2
x
5) f(x) = - 16
= (x - 4)(x + 4)
2
x
5) f(x) = - 16
= (x - 4)(x + 4)
zeros: 4, -4
6) f(x) = x2 + 12x + 36
6) f(x) = x2 + 12x + 36
= (x )(x )
6) f(x) = x2 + 12x + 36
= (x + 6)(x + 6)
6) f(x) = x2 + 12x + 36
= (x + 6)(x + 6)
zeros: -6, -6
7) f(x) = 2x2 - 14x + 24
7) f(x) = 2x2 - 14x + 24
= 2(
)
7) f(x) = 2x2 - 14x + 24
2
= 2(x - 7x + 12)
7) f(x) = 2x2 - 14x + 24
2
= 2(x - 7x + 12)
= 2(x )(x )
7) f(x) = 2x2 - 14x + 24
2
= 2(x - 7x + 12)
= 2(x - 4)(x - 3)
7) f(x) = 2x2 - 14x + 24
2
= 2(x - 7x + 12)
= 2(x - 4)(x - 3)
zeros: 4, 3
8) f(x) =
x4 - x3 - 20x2
8) f(x) = x4 - x3 - 20x2
2
=x (
)
8) f(x) = x4 - x3 - 20x2
2
2
= x (x - x - 20x)
8) f(x) = x4 - x3 - 20x2
2
2
= x (x - x - 20x)
2
= x (x )(x )
8) f(x) = x4 - x3 - 20x2
2
2
= x (x - x - 20x)
2
= x (x + 4)(x - 5)
8) f(x) = x4 - x3 - 20x2
2
2
= x (x - x - 20x)
2
= x (x + 4)(x - 5)
= (x)(x)(x + 4)(x - 5)
8) f(x) = x4 - x3 - 20x2
2
2
= x (x - x - 20x)
2
= x (x + 4)(x - 5)
= (x)(x)(x + 4)(x - 5)
zeros: 0, 0, -4, 5
Find a polynomial with the following zeros.
9)
-7, 2
Find a polynomial with the following zeros.
9)
-7, 2
(x - -7)(x - 2)
Find a polynomial with the following zeros.
9)
-7, 2
(x - -7)(x - 2)
(x + 7)(x - 2)
Find a polynomial with the following zeros.
9)
-7, 2
(x - -7)(x - 2)
(x + 7)(x - 2)
x2 - 2x + 7x - 14
Find a polynomial with the following zeros.
9)
-7, 2
(x - -7)(x - 2)
(x + 7)(x - 2)
x2 - 2x + 7x - 14
x2 + 5x - 14
10) 0, 4
10) 0, 4
(x - 0)(x - 4)
10) 0, 4
(x - 0)(x - 4)
x(x - 4)
10) 0, 4
(x - 0)(x - 4)
x(x - 4)
x2 - 4x
What does the graph of each function look like? (circle two for each)
11)
f(x) = -x2 + 6x + 9
rises to the left
rises to the right
falls to the left
falls to the right
What does the graph of each function look like? (circle two for each)
11)
f(x) = -x2 + 6x + 9
rises to the left
rises to the right
falls to the left
falls to the right
What does the graph of each function look like? (circle two for each)
11)
f(x) = -x2 + 6x + 9
rises to the left
rises to the right
falls to the left
falls to the right
12)
f(x) = 0.5x3 + 2x
rises to the left
falls to the left
rises to the right
falls to the right
12)
f(x) = 0.5x3 + 2x
rises to the left
falls to the left
rises to the right
falls to the right
12)
f(x) = 0.5x3 + 2x
rises to the left
falls to the left
rises to the right
falls to the right
13)
f(x) = 6(x4 + 3x2 + 2) rises to the left
falls to the left
rises to the right
falls to the right
13)
f(x) = 6(x4 + 3x2 + 2) rises to the left
falls to the left
rises to the right
falls to the right
13)
f(x) = 6(x4 + 3x2 + 2) rises to the left
falls to the left
rises to the right
falls to the right
14)
f(x) = -x5 - 7x + 10
rises to the left
falls to the left
rises to the right
falls to the right
14)
f(x) = -x5 - 7x + 10
rises to the left
falls to the left
rises to the right
falls to the right
14)
f(x) = -x5 - 7x + 10
rises to the left
falls to the left
rises to the right
falls to the right
Use long division to simplify.
15)
(2x3 - 3x2 - 50x + 75) / (2x - 3)
Use long division to simplify.
15)
(2x3 - 3x2 - 50x + 75) / (2x - 3)
2x - 3 2x3 - 3x2 - 50x + 75
Use long division to simplify.
15)
(2x3 - 3x2 - 50x + 75) / (2x - 3)
x2
2x - 3 2x3 - 3x2 - 50x + 75
Use long division to simplify.
15)
(2x3 - 3x2 - 50x + 75) / (2x - 3)
x2
2x - 3 2x3 - 3x2 - 50x + 75
2x3 - 3x2
Use long division to simplify.
15)
(2x3 - 3x2 - 50x + 75) / (2x - 3)
x2
2x - 3 2x3 - 3x2 - 50x + 75
2x3 - 3x2
0
0
Use long division to simplify.
15)
(2x3 - 3x2 - 50x + 75) / (2x - 3)
x2
2x - 3 2x3 - 3x2 - 50x + 75
2x3 - 3x2
0
0 - 50x + 75
Use long division to simplify.
15)
(2x3 - 3x2 - 50x + 75) / (2x - 3)
x2 - 25
2x - 3 2x3 - 3x2 - 50x + 75
2x3 - 3x2
0
0 - 50x + 75
Use long division to simplify.
15)
(2x3 - 3x2 - 50x + 75) / (2x - 3)
x2 - 25
2x - 3 2x3 - 3x2 - 50x + 75
2x3 - 3x2
0
0 - 50x + 75
- 50x + 75
Use long division to simplify.
15)
(2x3 - 3x2 - 50x + 75) / (2x - 3)
x2 - 25
2x - 3 2x3 - 3x2 - 50x + 75
2x3 - 3x2
0
0 - 50x + 75
- 50x + 75
0
0
Use long division to simplify.
15)
(2x3 - 3x2 - 50x + 75) / (2x - 3)
x2 - 25
2x - 3 2x3 - 3x2 - 50x + 75
2x3 - 3x2
0
0 - 50x + 75
- 50x + 75
0
0
Use synthetic division to simplify.
16)
(3x3 - 17x2 + 15x - 25) / (x - 5)
Use synthetic division to simplify.
16)
(3x3 - 17x2 + 15x - 25) / (x - 5)
3 -17
15
-25
Use synthetic division to simplify.
16)
(3x3 - 17x2 + 15x - 25) / (x - 5)
5
3 -17
15
-25
Use synthetic division to simplify.
16)
(3x3 - 17x2 + 15x - 25) / (x - 5)
5
3 -17
3
15
-25
Use synthetic division to simplify.
16)
(3x3 - 17x2 + 15x - 25) / (x - 5)
5
3 -17
15
3
15
-25
Use synthetic division to simplify.
16)
(3x3 - 17x2 + 15x - 25) / (x - 5)
5
3 -17
15
3 -2
15
-25
Use synthetic division to simplify.
16)
(3x3 - 17x2 + 15x - 25) / (x - 5)
5
3 -17 15
15 -10
3 -2
-25
Use synthetic division to simplify.
16)
(3x3 - 17x2 + 15x - 25) / (x - 5)
5
3 -17 15
15 -10
3 -2
5
-25
Use synthetic division to simplify.
16)
(3x3 - 17x2 + 15x - 25) / (x - 5)
5
3 -17 15
15 -10
3 -2
5
-25
25
Use synthetic division to simplify.
16)
(3x3 - 17x2 + 15x - 25) / (x - 5)
5
3 -17 15
15 -10
3 -2
5
-25
25
0
Use synthetic division to simplify.
16)
(3x3 - 17x2 + 15x - 25) / (x - 5)
5
3 -17 15
15 -10
3 -2
5
3x2 - 2x + 5
-25
25
0
17)
(2x3 + 14x2 - 20x + 7) / (x + 6)
17)
(2x3 + 14x2 - 20x + 7) / (x + 6)
2
14
-20
7
(2x3 + 14x2 - 20x + 7) / (x + 6)
17)
-6
2
14
-20
7
(2x3 + 14x2 - 20x + 7) / (x + 6)
17)
-6
2
2
14
-12
2
-20 7
-12 192
-32 199
(2x3 + 14x2 - 20x + 7) / (x + 6)
17)
-6
2
2
14
-12
2
-20 7
-12 192
-32 199
2x2 + 2x - 32 + 199
x+6
Write in completely factored form. Then find all zeros.
18)
f(x) = x3 + 4x2 - 25x - 28
Hint: (x - 4) is a factor
Write in completely factored form. Then find all zeros.
18)
f(x) = x3 + 4x2 - 25x - 28
Hint: (x - 4) is a factor
1
4
-25 -28
Write in completely factored form. Then find all zeros.
18)
f(x) = x3 + 4x2 - 25x - 28
Hint: (x - 4) is a factor
4 1
4
-25 -28
Write in completely factored form. Then find all zeros.
18)
f(x) = x3 + 4x2 - 25x - 28
Hint: (x - 4) is a factor
4 1
1
4 -25 -28
4 32 28
8
7
0
Write in completely factored form. Then find all zeros.
18)
f(x) = x3 + 4x2 - 25x - 28
Hint: (x - 4) is a factor
4 1
1
4 -25 -28
4 32 28
8
7
0
x2 + 8x + 7
Write in completely factored form. Then find all zeros.
18)
f(x) = x3 + 4x2 - 25x - 28
Hint: (x - 4) is a factor
4 1
1
4 -25 -28
4 32 28
8
7
0
x2 + 8x + 7
(x + 1)(x + 7)
Write in completely factored form. Then find all zeros.
18)
f(x) = x3 + 4x2 - 25x - 28
Hint: (x - 4) is a factor
4 1
1
4 -25 -28
4 32 28
8
7
0
x2 + 8x + 7
(x + 1)(x + 7)
(x - 4)(x + 1)(x + 7)
Write in completely factored form. Then find all zeros.
18)
f(x) = x3 + 4x2 - 25x - 28
Hint: (x - 4) is a factor
4 1
1
4 -25 -28
4 32 28
8
7
0
x2 + 8x + 7
(x + 1)(x + 7)
(x - 4)(x + 1)(x + 7)
zeros: 4, -1,
-7
19)
f(x) = x4 - 4x3 - 7x2 + 22x + 24
Hint: (x + 2) and (x - 3) are factors
19)
f(x) = x4 - 4x3 - 7x2 + 22x + 24
1 -4 -7
22 24
Hint: (x + 2) and (x - 3) are factors
f(x) = x4 - 4x3 - 7x2 + 22x + 24
19)
3
1 -4 -7 22 24
3 -3 -30 -24
1 -1 -10 -8 0
Hint: (x + 2) and (x - 3) are factors
f(x) = x4 - 4x3 - 7x2 + 22x + 24
19)
3
1 -4 -7 22 24
3 -3 -30 -24
1 -1 -10 -8 0
x3 - x2 - 10x - 8
Hint: (x + 2) and (x - 3) are factors
f(x) = x4 - 4x3 - 7x2 + 22x + 24
19)
3
1 -4 -7 22 24
3 -3 -30 -24
1 -1 -10 -8 0
x3 - x2 - 10x - 8
1 -1 -10 -8
Hint: (x + 2) and (x - 3) are factors
f(x) = x4 - 4x3 - 7x2 + 22x + 24
19)
3
-2
1 -4 -7 22 24
3 -3 -30 -24
1 -1 -10 -8 0
x3 - x2 - 10x - 8
1 -1 -10 -8
Hint: (x + 2) and (x - 3) are factors
f(x) = x4 - 4x3 - 7x2 + 22x + 24
19)
3
-2
1 -4 -7 22 24
3 -3 -30 -24
1 -1 -10 -8 0
x3 - x2 - 10x - 8
1 -1 -10 -8
-2 6 8
1 -3 -4 0
Hint: (x + 2) and (x - 3) are factors
f(x) = x4 - 4x3 - 7x2 + 22x + 24
19)
3
-2
1 -4 -7 22 24
3 -3 -30 -24
1 -1 -10 -8 0
x3 - x2 - 10x - 8
1 -1 -10 -8
-2 6 8
1 -3 -4 0
x2 - 3x - 4
Hint: (x + 2) and (x - 3) are factors
f(x) = x4 - 4x3 - 7x2 + 22x + 24
19)
3
-2
1 -4 -7 22 24
3 -3 -30 -24
1 -1 -10 -8 0
x3 - x2 - 10x - 8
1 -1 -10 -8
-2 6 8
1 -3 -4 0
x2 - 3x - 4
(x - 4)(x + 1)
Hint: (x + 2) and (x - 3) are factors
f(x) = x4 - 4x3 - 7x2 + 22x + 24
19)
3
-2
1 -4 -7 22 24
3 -3 -30 -24
1 -1 -10 -8 0
x3 - x2 - 10x - 8
1 -1 -10 -8
-2 6 8
1 -3 -4 0
x2 - 3x - 4
(x - 4)(x + 1)
(x - 4)(x + 1)(x + 2)(x - 3)
Hint: (x + 2) and (x - 3) are factors
f(x) = x4 - 4x3 - 7x2 + 22x + 24
19)
3
1 -4 -7 22 24
3 -3 -30 -24
1 -1 -10 -8 0
x3 - x2 - 10x - 8
-2
1 -1 -10 -8
-2 6 8
1 -3 -4 0
x2 - 3x - 4
(x - 4)(x + 1)
(x - 4)(x + 1)(x + 2)(x - 3)
zeros: 4, -1,
-2,
3
Hint: (x + 2) and (x - 3) are factors
Write each complex number in standard form.
20)
(3 + 2i) + (5 + i)
Write each complex number in standard form.
20)
(3 + 2i) + (5 + i)
8 + 3i
21)
(3 + 2i)(5 + i)
21)
(3 + 2i)(5 + i)
15 + 3i + 10i + 2i2
21)
(3 + 2i)(5 + i)
15 + 3i + 10i + 2i2
15 + 13i + 2i2
21)
(3 + 2i)(5 + i)
15 + 3i + 10i + 2i2
15 + 13i + 2i2
15 + 13i + 2(-1)
21)
(3 + 2i)(5 + i)
15 + 3i + 10i + 2i2
15 + 13i + 2i2
15 + 13i + 2(-1)
13 + 13i
22)
(3 + 2i)
(5 + i)
22)
(3 + 2i) * (5 - i)
(5 + i) * (5 - i)
22)
(3 + 2i) * (5 - i) = 15 - 3i + 10i - 2i2
(5 + i) * (5 - i) = 25 + 5i - 5i - i2
22)
(3 + 2i) * (5 - i) = 15 - 3i + 10i - 2i2 = 15 + 7i -2(-1)
(5 + i) * (5 - i) = 25 + 5i - 5i - i2
22)
(3 + 2i) * (5 - i) = 15 - 3i + 10i - 2i2 = 15 + 7i -2(-1)
(5 + i) * (5 - i) = 25 + 5i - 5i - i2 = 25 - (-1)
22)
(3 + 2i) * (5 - i) = 15 - 3i + 10i - 2i2 = 15 + 7i -2(-1) = 17 + 7i
26
(5 + i) * (5 - i) = 25 + 5i - 5i - i2 = 25 - (-1)
22)
(3 + 2i) * (5 - i) = 15 - 3i + 10i - 2i2 = 15 + 7i -2(-1) = 17 + 7i
26
(5 + i) * (5 - i) = 25 + 5i - 5i - i2 = 25 - (-1)
17
26
+ 7 i
26
Find all zeros. Then rewrite the function in completely factored form.
23)
f(x) = x2 - 10x + 6
Find all zeros. Then rewrite the function in completely factored form.
23)
f(x) = x2 - 10x + 6
A=1
B = -10
C=6
Find all zeros. Then rewrite the function in completely factored form.
23)
f(x) = x2 - 10x + 6
A=1
B = -10
C=6
Find all zeros. Then rewrite the function in completely factored form.
23)
f(x) = x2 - 10x + 6
A=1
B = -10
C=6
Find all zeros. Then rewrite the function in completely factored form.
23)
f(x) = x2 - 10x + 6
A=1
B = -10
C=6
Find all zeros. Then rewrite the function in completely factored form.
23)
f(x) = x2 - 10x + 6
A=1
B = -10
C=6
Find all zeros. Then rewrite the function in completely factored form.
23)
f(x) = x2 - 10x + 6
A=1
B = -10
C=6
=
Find all zeros. Then rewrite the function in completely factored form.
23)
f(x) = x2 - 10x + 6
A=1
B = -10
C=6
=
24)
f(x) = x2 + 2x + 4
24)
f(x) = x2 + 2x + 4
Quadratic Formula
24)
f(x) = x2 + 2x + 4
Quadratic Formula ---------> Magic Happens
24)
f(x) = x2 + 2x + 4
Quadratic Formula ---------> Magic Happens ------------>
24)
f(x) = x2 + 2x + 4
Quadratic Formula ---------> Magic Happens ------------>
25)
f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
25)
f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
25)
-1
f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
3
-4 7 10
-3 7 -14
3 -7 14 -4
3x3 - 7x2 + 14x - 4
-4
4
0
25)
-1
f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
3
-4 7 10
-3 7 -14
3 -7 14 -4
3x3 - 7x2 + 14x - 4
-4
4
0
25)
-1
f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
3
-4 7 10
-3 7 -14
3 -7 14 -4
3x3 - 7x2 + 14x - 4
-4
4
0
3x3 - 7x2 + 14x - 4
25)
-1
f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
3
-4 7 10
-3 7 -14
3 -7 14 -4
3x3 - 7x2 + 14x - 4
-4
4
0
1/3
3x3 - 7x2 + 14x - 4
3 -7
14 -4
1
-2 4
3
-6
12 0
3x2 - 6x + 12
25)
-1
f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
3
-4 7 10
-3 7 -14
3 -7 14 -4
3x3 - 7x2 + 14x - 4
Quadratic Formula
-4
4
0
1/3
3x3 - 7x2 + 14x - 4
3 -7
14 -4
1
-2 4
3
-6
12 0
3x2 - 6x + 12
25)
-1
f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
3
-4 7 10
-3 7 -14
3 -7 14 -4
3x3 - 7x2 + 14x - 4
-4
4
0
1/3
3x3 - 7x2 + 14x - 4
3 -7
14 -4
1
-2 4
3
-6
12 0
3x2 - 6x + 12
Quadratic Formula -------> Magic Happens
25)
x=
-1
f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
3
-4 7 10
-3 7 -14
3 -7 14 -4
3x3 - 7x2 + 14x - 4
-4
4
0
x = 1/3
3x3 - 7x2 + 14x - 4
3 -7
14 -4
1
-2 4
3
-6
12 0
3x2 - 6x + 12
Quadratic Formula -------> Magic Happens ------->
25)
x=
-1
f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
3
-4 7 10
-3 7 -14
3 -7 14 -4
3x3 - 7x2 + 14x - 4
-4
4
0
x = 1/3
3x3 - 7x2 + 14x - 4
3 -7
14 -4
1
-2 4
3
-6
12 0
3x2 - 6x + 12
Quadratic Formula -------> Magic Happens ------->
26)
f(x) = x3 - 4x2 + 6x - 4
26)
f(x) = x3 - 4x2 + 6x - 4
26)
f(x) = x3 - 4x2 + 6x - 4
2, ____, ____
26)
f(x) = x3 - 4x2 + 6x - 4
2, ____, ____
Synthetic Division
26)
f(x) = x3 - 4x2 + 6x - 4
2, ____, ____
Synthetic Division ------> x2 - 2x + 2
26)
f(x) = x3 - 4x2 + 6x - 4
2, ____, ____
Synthetic Division ------> x2 - 2x + 2 ------> Quadratic Formula
26)
f(x) = x3 - 4x2 + 6x - 4
2, 1 + i, 1 - i
Synthetic Division ------> x2 - 2x + 2 ------> Quadratic Formula
26)
f(x) = x3 - 4x2 + 6x - 4
2, 1 + i, 1 - i
(x - 2)(x - 1 - i)(x - 1 + i)
Synthetic Division ------> x2 - 2x + 2 ------> Quadratic Formula
Find a polynomial with the following zeros.
27)
2 + 3i, 2 - 3i
(x - (2+3i))(x - (2 - 3i))
(x - 2 - 3i)(x - 2 + 3i)
x2 - 2x + 3ix
Find a polynomial with the following zeros.
27)
2 + 3i, 2 - 3i
(x - (2+3i))(x - (2 - 3i))
(x - 2 - 3i)(x - 2 + 3i)
x2 - 2x + 3ix - 2x + 4 - 6i
Find a polynomial with the following zeros.
27)
2 + 3i, 2 - 3i
(x - (2+3i))(x - (2 - 3i))
(x - 2 - 3i)(x - 2 + 3i)
x2 - 2x + 3ix - 2x + 4 - 6i - 3ix + 6i - 9i2
Find a polynomial with the following zeros.
27)
2 + 3i, 2 - 3i
(x - (2+3i))(x - (2 - 3i))
(x - 2 - 3i)(x - 2 + 3i)
x2 - 2x + 3ix - 2x + 4 - 6i - 3ix + 6i - 9i2
x2 - 2x + 3ix - 2x + 4 - 6i - 3ix + 6i - 9(-1)
Find a polynomial with the following zeros.
27)
2 + 3i, 2 - 3i
(x - (2+3i))(x - (2 - 3i))
(x - 2 - 3i)(x - 2 + 3i)
x2 - 2x + 3ix - 2x + 4 - 6i - 3ix + 6i - 9i2
x2 - 2x + 3ix - 2x + 4 - 6i - 3ix + 6i - 9(-1)
x2 - 4x + 4 + 9
Find a polynomial with the following zeros.
27)
2 + 3i, 2 - 3i
(x - (2+3i))(x - (2 - 3i))
(x - 2 - 3i)(x - 2 + 3i)
x2 - 2x + 3ix - 2x + 4 - 6i - 3ix + 6i - 9i2
x2 - 2x + 3ix - 2x + 4 - 6i - 3ix + 6i - 9(-1)
x2 - 4x + 4 + 9
x2 - 4x + 13
28)
0, 3, 5i, -5i
28)
0, 3, 5i, -5i
(x) (x-3) (x-5i) (x+5i)
28)
0, 3, 5i, -5i
(x) (x-3) (x-5i) (x+5i)
( x2 - 3x ) (x2 + 5ix - 5ix - 25i2 )
28)
0, 3, 5i, -5i
(x) (x-3) (x-5i) (x+5i)
( x2 - 3x ) (x2 + 5ix - 5ix - 25i2 )
( x2 - 3x ) (x2 + 25)
28)
0, 3, 5i, -5i
(x) (x-3) (x-5i) (x+5i)
( x2 - 3x ) (x2 + 5ix - 5ix - 25i2 )
( x2 - 3x ) (x2 + 25)
x4 + 25x2 - 3x3 - 75x
28)
0, 3, 5i, -5i
(x) (x-3) (x-5i) (x+5i)
( x2 - 3x ) (x2 + 5ix - 5ix - 25i2 )
( x2 - 3x ) (x2 + 25)
x4 + 25x2 - 3x3 - 75x
x4 - 3x3 + 25x2 - 75x
Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
29)
Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
29)
HA:
y = -1
VA:
x = -3
Holes: none
Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
30)
Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
30)
HA:
y=4
VA:
x=8
Holes: none
Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
31)
Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
31)
HA:
y=0
VA:
x = -3, x = 6
Holes: none
Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
32)
Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
32)
HA:
y=0
VA:
x = -1, x = 1
Holes: none
Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
33)
Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
33)
HA:
y=3
VA:
none
Holes: none
Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
34)
hint: this one has a hole
Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
34)
hint: this one has a hole
(x - 4)(x - 1)
(x + 1)(x - 1)
HA:
y=1
VA:
x = -1
Holes: x = 1
Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
35)
hint: this one has a hole
Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
35)
hint: this one has a hole
(2x - 1)(x - 3)
(2x + 3)(x - 3)
HA:
y=1
VA:
x = -1.5
Holes: x = 3
36)
This table shows the amounts A (in dollars) spent per
person on the internet in the United States from 2000 to
2005. Use a graphing calculator to create a scatter plot
of the data. Let t represent the year, with t = 0
corresponding to 2000.
a) Calculate a quadratic regression line to fit the data.
What is its equation?
b) Based on your quadratic model, approximate how
much was spent on each person in 2008.
Year
Amount, A
(in hours)
2000
3492
2001
3540
2002
3606
2003
3663
2004
3757
2005
3809
36)
This table shows the amounts A (in dollars) spent per
person on the internet in the United States from 2000 to
2005. Use a graphing calculator to create a scatter plot
of the data. Let t represent the year, with t = 0
corresponding to 2000.
a) Calculate a quadratic regression line to fit the data.
What is its equation?
f(x) = 2.36t2 + 53.7t + 3489
b) Based on your quadratic model, approximate how
much was spent on each person in 2008.
Year
Amount, A
(in hours)
2000
3492
2001
3540
2002
3606
2003
3663
2004
3757
2005
3809