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) = x2 - 16

5) f(x) = x2 - 16 = (x )(x )

5) f(x) = x2 - 16 = (x - 4)(x + 4)

5) f(x) = x2 - 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(x2 - 7x + 12)

7) f(x) = 2x2 - 14x + 24 = 2(x2 - 7x + 12) = 2(x )(x )

7) f(x) = 2x2 - 14x + 24 = 2(x2 - 7x + 12) = 2(x - 4)(x - 3)

7) f(x) = 2x2 - 14x + 24 = 2(x2 - 7x + 12) = 2(x - 4)(x - 3) zeros: 4, 3

8) f(x) = x4 - x3 - 20x2

8) f(x) = x4 - x3 - 20x2

= x2( )

8) f(x) = x4 - x3 - 20x2

= x2(x2 - x - 20x)

8) f(x) = x4 - x3 - 20x2

= x2(x2 - x - 20x) = x2(x )(x )

8) f(x) = x4 - x3 - 20x2

= x2(x2 - x - 20x) = x2(x + 4)(x - 5)

8) f(x) = x4 - x3 - 20x2

= x2(x2 - x - 20x) = x2(x + 4)(x - 5) = (x)(x)(x + 4)(x - 5)

8) f(x) = x4 - x3 - 20x2

= x2(x2 - x - 20x) = x2(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 - 14x2 + 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 rises to the rightfalls to the left falls to the right

12) f(x) = 0.5x3 + 2x rises to the left rises to the rightfalls to the left falls to the right

12) f(x) = 0.5x3 + 2x rises to the left rises to the rightfalls to the left falls to the right

13) f(x) = 6(x4 + 3x2 + 2) rises to the left rises to the rightfalls to the left falls to the right

13) f(x) = 6(x4 + 3x2 + 2) rises to the left rises to the rightfalls to the left falls to the right

13) f(x) = 6(x4 + 3x2 + 2) rises to the left rises to the rightfalls to the left falls to the right

14) f(x) = -x5 - 7x + 10 rises to the left rises to the rightfalls to the left falls to the right

14) f(x) = -x5 - 7x + 10 rises to the left rises to the rightfalls to the left falls to the right

14) f(x) = -x5 - 7x + 10 rises to the left rises to the rightfalls to the left 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 - 252x - 3 2x3 - 3x2 - 50x + 75 2x3 - 3x2

0 0 - 50x + 75

Use long division to simplify.15) (2x3 - 3x2 - 50x + 75) / (2x - 3)

x2 - 252x - 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 - 252x - 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 - 252x - 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 15 -25 3

Use synthetic division to simplify.16) (3x3 - 17x2 + 15x - 25) / (x - 5)

5 3 -17 15 -25 15 3

Use synthetic division to simplify.16) (3x3 - 17x2 + 15x - 25) / (x - 5)

5 3 -17 15 -25 15 3 -2

Use synthetic division to simplify.16) (3x3 - 17x2 + 15x - 25) / (x - 5)

5 3 -17 15 -25 15 -10 3 -2

Use synthetic division to simplify.16) (3x3 - 17x2 + 15x - 25) / (x - 5)

5 3 -17 15 -25 15 -10 3 -2 5

Use synthetic division to simplify.16) (3x3 - 17x2 + 15x - 25) / (x - 5)

5 3 -17 15 -25 15 -10 25 3 -2 5

Use synthetic division to simplify.16) (3x3 - 17x2 + 15x - 25) / (x - 5)

5 3 -17 15 -25 15 -10 25 3 -2 5 0

Use synthetic division to simplify.16) (3x3 - 17x2 + 15x - 25) / (x - 5)

5 3 -17 15 -25 15 -10 25 3 -2 5 0

3x2 - 2x + 5

17) (2x3 + 14x2 - 20x + 7) / (x + 6)

17) (2x3 + 14x2 - 20x + 7) / (x + 6)

2 14 -20 7

17) (2x3 + 14x2 - 20x + 7) / (x + 6)

-6 2 14 -20 7

17) (2x3 + 14x2 - 20x + 7) / (x + 6)

-6 2 14 -20 7 -12 -12 192 2 2 -32 199

17) (2x3 + 14x2 - 20x + 7) / (x + 6)

-6 2 14 -20 7 -12 -12 192 2 2 -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 4 -25 -28 4 32 28 1 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 4 -25 -28 4 32 28 1 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 4 -25 -28 4 32 28 1 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 4 -25 -28 4 32 28 1 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 4 -25 -28 4 32 28 1 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 Hint: (x + 2) and (x - 3) are factors

1 -4 -7 22 24

19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors

3 1 -4 -7 22 24 3 -3 -30 -24 1 -1 -10 -8 0

19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors

3 1 -4 -7 22 24 3 -3 -30 -24 1 -1 -10 -8 0 x3 - x2 - 10x - 8

19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors

3 1 -4 -7 22 24 3 -3 -30 -24 1 -1 -10 -8 0 x3 - x2 - 10x - 8 1 -1 -10 -8

19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors

3 1 -4 -7 22 24 3 -3 -30 -24 1 -1 -10 -8 0 x3 - x2 - 10x - 8 -2 1 -1 -10 -8

19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors

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

19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors

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

19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors

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)

19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors

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)

19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors

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

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) = (5 + i) * (5 - i) = 25 + 5i - 5i - i2 = 25 - (-1)

17 + 7i 26

22) (3 + 2i) * (5 - i) = 15 - 3i + 10i - 2i2 = 15 + 7i -2(-1) = (5 + i) * (5 - i) = 25 + 5i - 5i - i2 = 25 - (-1)

17 + 7i 26

17 + 7 i26 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 = 1B = -10C = 6

Find all zeros. Then rewrite the function in completely factored form.23) f(x) = x2 - 10x + 6

A = 1B = -10C = 6

Find all zeros. Then rewrite the function in completely factored form.23) f(x) = x2 - 10x + 6

A = 1B = -10C = 6

Find all zeros. Then rewrite the function in completely factored form.23) f(x) = x2 - 10x + 6

A = 1B = -10C = 6

Find all zeros. Then rewrite the function in completely factored form.23) f(x) = x2 - 10x + 6

A = 1B = -10C = 6

Find all zeros. Then rewrite the function in completely factored form.23) f(x) = x2 - 10x + 6

A = 1B = -10C = 6

=

Find all zeros. Then rewrite the function in completely factored form.23) f(x) = x2 - 10x + 6

A = 1B = -10C = 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) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4

-1 3 -4 7 10 -4 -3 7 -14 4 3 -7 14 -4 0 3x3 - 7x2 + 14x - 4

25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4

-1 3 -4 7 10 -4 -3 7 -14 4 3 -7 14 -4 0 3x3 - 7x2 + 14x - 4

25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4

-1 3 -4 7 10 -4 -3 7 -14 4 3 -7 14 -4 0 3x3 - 7x2 + 14x - 4

3x3 - 7x2 + 14x - 4

25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4

-1 3 -4 7 10 -4 1/3 3 -7 14 -4 -3 7 -14 4 1 -2 4 3 -7 14 -4 0 3 -6 12 0 3x3 - 7x2 + 14x - 4 3x2 - 6x + 12

3x3 - 7x2 + 14x - 4

25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4

-1 3 -4 7 10 -4 1/3 3 -7 14 -4 -3 7 -14 4 1 -2 4 3 -7 14 -4 0 3 -6 12 0 3x3 - 7x2 + 14x - 4 3x2 - 6x + 12

Quadratic Formula

3x3 - 7x2 + 14x - 4

25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4

-1 3 -4 7 10 -4 1/3 3 -7 14 -4 -3 7 -14 4 1 -2 4 3 -7 14 -4 0 3 -6 12 0 3x3 - 7x2 + 14x - 4 3x2 - 6x + 12

Quadratic Formula -------> Magic Happens

3x3 - 7x2 + 14x - 4

25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4

-1 3 -4 7 10 -4 1/3 3 -7 14 -4 -3 7 -14 4 1 -2 4 3 -7 14 -4 0 3 -6 12 0 3x3 - 7x2 + 14x - 4 3x2 - 6x + 12

Quadratic Formula -------> Magic Happens ------->

3x3 - 7x2 + 14x - 4x = x =

25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4

-1 3 -4 7 10 -4 1/3 3 -7 14 -4 -3 7 -14 4 1 -2 4 3 -7 14 -4 0 3 -6 12 0 3x3 - 7x2 + 14x - 4 3x2 - 6x + 12

Quadratic Formula -------> Magic Happens ------->

3x3 - 7x2 + 14x - 4x = x =

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 + 9x2 - 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

HA: y = 1

VA: x = -1

Holes: x = 1

(x - 4)(x - 1)(x + 1)(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

HA: y = 1

VA: x = -1.5

Holes: x = 3

(2x - 1)(x - 3)(2x + 3)(x - 3)

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?

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 + 3489b) Based on your quadratic model, approximate how

much was spent on each person in 2008.