pre ap/tag algebra ii final exam revie fall final review solutions.pdfthese review problems are...

Pre‐AP/TAG Algebra II Fall 2007 Final Exam Review These review problems are taken from the “Chapter Tests” in the book at the end of each chapter. PDF’s of the pages WITH the solutions can be found on Mr. Youn’s TeacherWeb (www.mryoun.com). Chapter 1 – page 80, 1‐23 Chapter 2 – page 170, 1‐25 Chapter 3 – page 236, 4‐11, 19, 20 Chapter 4 – page 302, 5‐10, 14‐18, 21, 22, page 43‐46 with calculator Chapter 5 – page 396, 4‐16, 18‐20, 23‐26 Chapter 6 – page 478, 1‐20

C H A P T E R

1

80 Chapter 1 Foundations for Functions

1. Order 1. −

5 , -2, 0.95, - √ � 3 , and 1 from least to greatest. Then classify each number by the subsets of the real numbers to which it belongs.

Rewrite each set in the indicated notation.

2. interval notation 3. (-∞, 12 ⎤ ⎦ ; set-builder notation

Identify the property demonstrated by each equation.

4. x + y = y + x 5. 9 · 2 + 9 · 7 = 9 · (2 + 7) 6. x = (1)x

7. A company manufactures square windows that come in three sizes: 6 square feet, 8 square feet, and 15 square feet. Estimate the side length of each window to the nearest tenth of a foot. Then identify which window is the largest one that could fit in a wall with a width of 3 feet.

Simplify each expression.

8. -2√ � 3 + √ � 75 9. √ � 24 - √ � 54 10. √ � 22 · √ � 55

11. 2 (x + 1) + 9x 12. 5x - 5y - 7x + y 13. 12x + 4 (x + y) - 6y

Simplify each expression. Assume all variables are nonzero.

14. 8a2b5(- 2a3b2) 15. 28u-2v3_ 4u2v2

16. ( 5x4y-3) -2

17. ( 3x2y_xy2 )

-1

18. German shepherds are often used as police dogs because they have 2.25 × 10 8 smell receptors in their nose. Humans average only 5 × 10 6 smell receptors in their nose. How many times as great is the number of smell receptors in a German shepherd’s nose as that in a human’s nose?

Give the domain and range for each relation. Then tell whether each relation is a function.

19. x 10 9 8 9 10

y 2 4 6 8 10

20.

For each function, evaluate f (-2) , f (1_2 ) , and f (0) .

21. f (x) = -4x 22. f (x) = -3x2 + x 23. f (x) = √ �� x + 3

24. The table shows how the distance from the top of a building to the horizon depends on the building’s height. Graph the relationship from building height to horizon distance, and identify which parent function best describes the data. Then use your graph to estimate the distance to the horizon from the top of a building with a height of 80 m.

Horizon Distances

Height of Building (m) 5 10 20 40 100

Distance to Horizon (km) 8.0 11.3 15.9 22.5 35.6

80

3√ � 3 - √ � 6 11√ � 10

45

(-∞, -2) and (1, 3]

D: ⎧ ⎨

⎩ 8, 9, 10

⎫ ⎬

⎭ ; R: ⎧

⎨

⎩ 2, 4, 6, 8, 10

⎫ ⎬

⎭ ;

not a function

D: [-5, 5];R: [-2, 2];function

⎧ ⎨

⎩ x | x ≤ 12

⎫ ⎬

⎭

16x - 2y11x + 2

80 Chapter 1

OrganizerObjective: Assess students’ mastery of concepts and skills in Chapter 1.

Online Edition

ResourcesAssessment Resources

Chapter 1 Tests

• Free Response

(Levels A, B, C)

• Multiple Choice

(Levels A, B, C)

• Performance Assessment

IDEA Works! CD-ROM

Modified Chapter 1 Test

Answers 1. -2, - √ � 3, 0.95, 1, 1. − 5; -2: �, �,

�; - √ � 3: �, irrational; 0.95: �, �;1: �, �, �, , ; 1. − 5: �, �

4. Comm. Prop. of Add.

5. Distributive Property

6. Multiplicative Identity Property

7. 2.4 ft, 2.8 ft, and 3.9 ft; the 8 ft2

window is the largest that could fit in the wall.

12. -2x - 4y

14. -16 a5b7

15. 7v_u4

16.y6_

25 x8

17.y_3x

21. 8; -2; 0

22. -14; - 1_4

; 0

23. 1; ≈1.87; ≈1.73

24.

0 20 40 60 80

8

16

24

32

Height of building (m)

Dis

tanc

e to

hor

izon

(km

)

100

square-root function; ≈ 32 km

TAKS Practice Grades 9–11 Items

Obj. 1 19, 20

Obj. 2 12–17, 19–24

Obj. 5 14–18

Obj. 10 7, 18, 24

2 N D P R I N T

170 Chapter 2 Linear Functions

Solve.

1. 5 (3x - 4) - 12 = 73 2. 2x + 12 - 8x = 9 - x - 5x 3. 4 (3 - 3x) - 8x = 15 - 2(5x + 8)

4. -5_4

= 12_x 5. 3x - 9_

15 = 18_

12 6. 2_

2x - 5 = 3_

x + 1 7. Tim and Kim took 4.6 hours to complete a 25.3 mile kayaking trip. If they want to

paddle for 3 hours on their next trip, how far should they plan to go?

Graph.

8. y = 5_3

x - 4 9. 6x + 8y = 24 10. 6x + 2y < 10

Write the equation of each line in slope-intercept form.

11. passing through (9, 12) and (7, 2)12. parallel to 9x - 5y = 8 and through (-10, 2)

13. perpendicular to y = - 2__7x + 3 and through (6, 4)

14. The Spanish Club is selling T-shirts and hats and would like to raise at least $2400. It sells T-shirts for $15 and hats for $8. Write and graph an inequality representing the number of T-shirts and hats the club must sell to meet its goal.

Let g(x) be the indicated transformation(s) of f (x) = x. Write the rule for g(x) .

15. vertical stretch by a factor of 4 16. horizontal translation 6 units right

17. horizontal compression by a factor of 1__6 followed by a vertical shift 4 units down

18. A consumer group is studying how hospitals are staffed. Here are the results from eight randomly selected hospitals in a state.

Full-Time Hospital Employees

Hospital Beds 23 29 35 42 46 54 64 76

Full-TimeEmployees

69 95 118 126 123 178 156 176

a. Make a scatter plot of the data with hospital beds as the independent variable.

b. Find the correlation coefficient and the equation of the line of best fit. Draw the line of best fit on your scatter plot.

c. Predict the number of beds in a hospital with 80 full-time employees.

19. Solve ⎪12 + 4x⎥ - 6 = 26.

Solve and graph.

20. 16 ≤ 24 - 8x_5

21. ⎪3x - 9⎥ > 12 22. 3 ⎪12 - 4x⎥ + 4 ≤ 28

23. A pollster predicts the actual percent p of a population that favors a political candidate by using a sample percent s plus or minus 3%. Write an absolute-value inequality for p.

24. Translate f (x) = ⎪x⎥ so that its vertex is at (4, -2) . Then graph.

25. Find g(x) if f (x) = ⎪2x⎥ - 3 is stretched horizontally by a factor of 3 and reflected across the x-axis.

170

x = 7contradiction; ∅ x = 1.3

x = -9.6 x = 10.5

x = 5 or x = -11

x ≤ -7{x |x < -1 & x > 7} {x | 1 ≤ x ≤ 5}

y = 5x - 33

y = 9_5

x + 20

y = 7_2

x -17

g (x) = 4x g (x) = x - 6

g (x) = 6x - 4

g (x) = ⎪x - 4⎥ - 2

g (x) = - ⎪ 2x_3 ⎥ + 3

r ≈ 0.913; e ≈ 1.95b + 40.1 20 or 21

15Ts + 8h ≥ 2400

≈ 16.5 mi

⎪p - s⎥ < 3

x = 4.25


Online Edition


Chapter 2 Tests • Free Response

(Levels A, B, C)

• Multiple Choice

(Levels A, B, C)


IDEA Works! CD-ROM


Answers8.

170 Chapter 2

9.

10.

14.

18a.

20.

21.

22.

24.

C H A P T E R

2


Obj. 1 8–10, 14, 23, 24

Obj. 2 1–6, 18

Obj. 3 11–13

Obj. 7 11–13

Obj. 9 7, 23

Obj. 10 7, 10, 14, 18

2 N D P R I N T

232 Chapter 3 Linear Systems

consistent system . . . . . . . . . . . 183

constraint . . . . . . . . . . . . . . . . . . 205

dependent system . . . . . . . . . . 184

elimination . . . . . . . . . . . . . . . . 191

feasible region . . . . . . . . . . . . . . 205

inconsistent system . . . . . . . . . 183

independent system . . . . . . . . . 184

linear programming . . . . . . . . 205

linear system . . . . . . . . . . . . . . . 182

objective function . . . . . . . . . . 206

ordered triple . . . . . . . . . . . . . . . 214

parameter . . . . . . . . . . . . . . . . . . 230

parametric equations . . . . . . . 230

substitution . . . . . . . . . . . . . . . . 190

system of equations . . . . . . . . . 182

system of linear inequalities . . . . . . . . . . . . . . 199

three-dimensional coordinate system. . . . . . . . . . . . . . . . . . . 214

z-axis . . . . . . . . . . . . . . . . . . . . . . 214

Solve each system by using a graph and a table.

6.⎧ ⎨

⎩ y = 2x

3x - y = 57.

⎧ ⎨

⎩ x + y = 6

x - y = 2

8.⎧ ⎨

⎩ x - 6y = 2

2x - 5y = -39.

⎧ ⎨

⎩ x - 3y = 6

3x - y = 2

Classify each system and determine the number of solutions.

10.⎧ ⎨

⎩ y = x - 7

x + 9y = 1611.

⎧ D

⎨ D

⎩

1_2

x + 2y = 3

x + 4y = 6

12.⎧ ⎨

⎩ 5x - 10y = 8

x - 2y = 4 13.

⎧ ⎨

⎩ 4x - 3y = 21

2x - 2y = 10

14. Security A locksmith charges $25 to make a house call and $15 for each lock that is re-keyed. Another locksmith charges $10 to make a house call and $20 for each lock that is re-keyed. For how many locks will the total costs be the same?

■ Solve ⎧

⎨

⎩ x + y = 3

3x - 6y = -9 by using a graph and

a table.

Solve each equation for y.⎧

D

⎨

D

⎩ y = -x + 3

y = 1_2

x + 3_2

Make a table of values. Graph the lines.

y = -x + 3 y = 1_2

x + 3_2

x y

0 3

1 2

4 1

x y

0 1.5

1 2

4 2.5

The solution is (1, 2).

3-1 Using Graphs and Tables to Solve Linear Systems (pp. 182–189)

EXERCISESE X A M P L E S

Complete the sentences below with vocabulary words from the list above.

1. A consistent and −−−−−− ? system has infinitely many solutions.

2. −−−−−− ? involves adding or subtracting equations to get rid of one of the variables in a system.

3. In a linear programming problem, the solution to the −−−−−− ? can be graphed as a(n) −−−−−− ? .

4. Each point in a(n) −−−−−− ? can be represented by a(n) −−−−−− ? .

5. A(n) −−−−−− ? system is a set of equations or inequalities that has at least one solution.

Vocabulary

236 Chapter 3 Linear Systems

Solve each system by using a graph and a table.

1.⎧ D ⎨

D ⎩ x - y = -4

3x - 6y = -12 2.

⎧ D ⎨

D ⎩ y = x - 1

x + 4y = 63.

⎧

⎨

⎩

x - y = 3

2x + 3y = 6

Classify each system and determine the number of solutions.

4.⎧ D

⎨

D ⎩ 6y = 9x

8x + 4y = 205.

⎧ D

⎨

D ⎩ 12x + 3y = -9

-y - 4x = 3 6.

⎧ D

⎨

D ⎩ 3x - 9y = 21

6 = x - 3y

Use substitution or elimination to solve each system of equations.

7.⎧ D

⎨ D ⎩ y = x - 2

x + 5y = 20 8.

⎧ D

⎨

D ⎩ 5x - y = 33

7x + y = 51 9.

⎧ D ⎨

D ⎩ x + y = 5

2x + 5y = 16

Graph each system of inequalities.

10.⎧ D ⎨

D ⎩ 2y - 4x ≥ 4

y - x ≥ 1 11.

⎧ D ⎨

D ⎩ x + y ≥ 3

y - 4 ≤ 0

12. Chemistry A chemist wants to mix a new solution with at least 18% pure salt. The chemist has two solutions with 9% pure salt and 24% pure salt and wants to make at most 250 mL of the new solution. Write and graph a system of inequalities that can be used to find the amounts of each salt solution needed.

13. Minimize the objective function P = 5x + 9y under the following constraints.

⎧

D

⎨ D

⎩

x ≥ 0y ≥ 0

y ≤ 2x + 1

y ≤ -3x + 6

Graph each point in three-dimensional space.

14. (2, -1, 3) 15. (0, -1, 3) 16. (-2, 1, -1)

Business Use the following information and the table for Problems 17 and 18.A plumber charges $50 for repairing a leaking faucet, $150 for installing a sink, and $200 for an emergency situation. The plumber’s total income was exactly $1000 for each day shown in the table.

17. Write a linear equation in three variables to represent this situation.

18. Complete the table for the possible numbers of tasks each day.

Solve each system of equations using elimination, or state that the system is inconsistent or dependent.

19.

⎧

D

⎨

D

⎩

x - y + z = -2

4x - y + 2z = -3

2x - 3y + 2z = -7

20.

⎧

D

⎨

D

⎩

3x - y - z = -1

x + y + 2z = 8

6x - 2y - 2z = 5

Day Repair Faucet Install Sink Emergency

Monday 2 2

Tuesday 3 2

Wednesday 1 4

Thursday 4 4

236

(-4, 0) (2, 1) (3, 0)

independent;one solution

dependent;infinitely many solutions

inconsistent;no solution

(5, 3) (7, 2) (3, 2)

P = 0

(-1, 3, 2) inconsistent

3

3

1

1

50x + 150y + 200z = 1000

236 Chapter 3


Online Edition


Chapter 3 Tests

• Free Response (Levels A, B, C)

• Multiple Choice (Levels A, B, C)


IDEA Works! CD-ROM


Answers 10.

11.

12.⎧

⎨

⎩

x + y ≤ 250

0.09x + 0.24y < 45 14–16.

C H A P T E R

3


Obj. 4 1–3, 7–12

Obj. 10 12, 17

2 N D P R I N T

302 Chapter 4 Matrices

Use the data from the table to answer the questions.

1. Display the data in the form of matrix A.

2. What are the dimensions of the matrix?

3. What is the value of the matrix entry with address a31?

4. What is the address of the entry that has a value of 2?

Evaluate, if possible.

E =

⎡

⎢

⎣

2 3

-1 04 1

⎤

�

⎦

F = ⎡ ⎢

⎣

4 -2 0-1 1 -2

⎤ �

⎦ G =

⎡

⎢

⎣ 2 -13 1

⎤ �

⎦ H =

⎡

⎢

⎣

-2 1

3 05 -1

⎤

�

⎦

J = ⎡

⎢

⎣ 1 -5 6

⎤ �

⎦ K =

⎡

⎢

⎣

70

-2

⎤

�

⎦

5. E + F 6. EF 7. FE

8. H 2 9. G 3 10. FK

Use a matrix to transform PQR.

11. Translate �PQR 2 units up and 1 unit right.

12. Enlarge �PQR by a factor of 3_2

.

13. Use ⎡

⎢

⎣ 0 22 0

⎤ �

⎦ to transform �PQR. Describe the image.

Find the determinant of each matrix.

14.⎡ ⎢

⎣ 4 00 -3

⎤ �

⎦ 15.

⎡

⎢

⎣ 0.25 1

2 8 ⎤ �

⎦ 16.

⎡ ⎢

⎣

3-2

-1-1

⎤

�

⎦ 17.

⎡

⎢

⎣

132

-2-1

1

3

-35

⎤

�

⎦

18. Use Cramer’s rule to solve ⎧

⎨

⎩ x + 2y = 1

3x - y = 10 19. Use Cramer’s rule to solve

⎧

�

⎨

�

⎩

x + 3z = 3 + 2y

3x + 22 = y + 3z

2x + y + 5z = 8

Find the inverse, if it exists.

20.⎡

⎢

⎣ 2 0.74 1.4

⎤ �

⎦ 21.

⎡

⎢

⎣ 3 -11 3

⎤ �

⎦ 22.

⎡

⎢

⎣ 3 12 -1

⎤ �

⎦ 23.

⎡

⎢

⎣ 3 2 -12 3 -51 4 2

⎤

�

⎦

24. The cost of 2.5 pounds of figs and 1.5 pounds of dates is $14.42. The cost of 3.5 pounds of figs and 1 pound of dates is $16.91. Use a matrix operation to find the price of each per pound.

Write the matrix equation for each system, and solve, if possible.

25.⎧ ⎨

⎩ 6x + y = 2

3x - 2y + 1 = 026.

⎧

⎨

⎩ 5x - 2y = 3

2.5x - y = 1.5

27.⎧

⎨

⎩ x + 2y = 3.5

3x = 2.7 + y

28.

⎧

�

⎨

�

⎩

2x - z = 3 + y

x + 2 = y + 5

4z + x + y = 1

Write the augmented matrix, and use row reduction to solve, if possible.

29. Use the data from Items 1–4 above. Find the number of points assigned for finishing in first, second, and third places.

Awards Given

FirstPlace

Second Place

Third Place

Total Points

Klete 5 1 2 41

Michael 3 5 1 42

Ryan 3 1 4 29

302

3 x 43

a 13

-12 0 -5

(3, -1) (-4, 1, 3)

no inverse

$3.98; $2.98

55

302 Chapter 4

8. not possible

9.⎡

⎢

⎣

-712

-411

⎤

�

⎦

10. ⎡

⎢

⎣

28

-3 ⎤

�

⎦

11. ⎡

⎢

⎣

-1

332

00

⎤

�

⎦

+

⎡

⎢

⎣

12

12

12

⎤

�

⎦

=

⎡

⎢

⎣

0 4 15 4 2

⎤

�

⎦

.

The coordinates of the image are P '(0, 5),Q'(4, 4), and R'(1, 2).

12. 3_2

⎡

⎢

⎣

-1

332

00

⎤

�

⎦

=

⎡

⎢

⎣

- 3__2

9__2

9__2

3

0

0

⎤

�

⎦

The coordinates of the

image are P' (- 3_2

, 9_2 ),

Q'(9_2

, 3), and R'(0, 0).

13. The coordinates of the image are (6, -2), (4, 6),and (0, 0). The triangle has been enlarged by a factor of 2 and reflected across the line y = x.

21.⎡

⎢

⎣

0.3

-0.10.10.3

⎤

�

⎦

22.⎡

⎢

⎣

0.20.4

0.2-0.6

⎤

�

⎦

23.⎡

⎢

⎣

0.47-0.16

0.09

-0.150.13

-0.18 -0.13

0.240.09

⎤

�

⎦

25–29. See p. A26.


Online Edition


Chapter 4 Tests




IDEA Works! CD-ROM


Answers

1. A =

⎡

⎢

⎣

5 1 2 413 5 1 423 1 4 29

⎤

�

⎦

5. The operation cannot be per-formed because the matrices do not have the same dimensions.

6.⎡

⎢

⎣

5-415

-12

-7

-60

-2

⎤

�

⎦

7.⎡

⎢

⎣

10

-1112

-5

⎤

�

⎦

C H A P T E R

4


Obj. 4 24–29

2 N D P R I N T

396 Chapter 5 Quadratic Functions

Using the graph of f (x) = x2 as a guide, describe the transformations, and then graph each function.

1. g (x) = (x + 1)2 - 2 2. h (x) = - 1_2

x2 + 2

3. Use the following description to write a quadratic function in vertex form: f(x) = x2

is vertically compressed by a factor of 1__2

and translated 6 units right to create g.

For each function, (a) determine whether the graph opens upward or downward, (b) find the axis of symmetry, (c) find the vertex, (d) find the y-intercept, and (e) graph the function.

4. f (x) = -x2 + 4x + 1 5. g (x) = x2 - 2x + 3

6. The area A of a rectangle with a perimeter of 32 cm is modeled by the function A(x) = -x2 + 16x, where x is the width of the rectangle in centimeters. What is the maximum area of the rectangle?

Find the roots of each equation by using factoring.

7. x2 - 2x + 1 = 0 8. x2 + 10x = -21

Solve each equation.

9. x2 + 4x = 12 10. x2 - 12x = 25

11. x2 + 25 = 0 12. x2 + 12x = -40

Write each function in vertex form, and identify its vertex.

13. f (x) = x2 - 4x + 9 14. g (x) = x2 - 18x + 92

Find the zeros of each function by using the Quadratic Formula.

15. f (x) = (x - 1)2 + 7 16. g (x) = 2 x2 - x + 5

17. The height h in feet of a person on a waterslide is modeled by the function h (t) = -0.025t2 - 0.5t + 50, where t is the time in seconds. At the bottom of the slide, the person lands in a swimming pool. To the nearest tenth of a second, how long does the ride last?

18. Graph the inequality y < x2 - 3x - 4.

Solve each inequality.

19. -x2 + 3x + 5 ≥ 7 20. x2 - 4x + 1 > 1

For Exercises 21 and 22, use the table showing the average cost of LCD televisions at one store.

21. Find a quadratic model for the cost of a television given its size.

22. Use the model to estimate the cost of a 42 in. LCD television.

Perform the indicated operation, and write the result in the form a + bi.

23. (12 - i) - (5 + 2i) 24. (6 - 2i)(2 - 2i) 25. -2i18 26. 1 - 8i_4i

Costs of LCD Televisions

Size (in.) 15 17 23 30

Cost ($) 550 700 1500 2500

396

g is f translated 1 unit left and 2 units down.

h is f reflected across the x-axis, vertically compressed by a factor of 1_

2 ,

and translated 2 units up.

downward; x = 2; (2, 5) ; 1 upward; x = 1; (1, 2) ; 3

64 cm 2

1 -3, -7

-6, 2 6 ± √ � 61

f(x) = (x - 2)2

+ 5; (2, 5)g(x) = (x - 9)

2+ 11; (9, 11)

±5i -6 ± 2i

1 ± i √ � 71_4 ±

√ � 39_4

i

1 ≤ x ≤ 2 x < 0 or x > 4

y ≈ 1.8x2+ 52x - 662

7 - 3i 8 - 16i2 -2 - 1_

4i

≈ 35.8 s

g(x) = 1_2

(x - 6)2

about $4697

396 Chapter 5


Online Edition


Chapter 5 Tests




IDEA Works! CD-ROM


Answers 1.

2.

4.

5.

18.

C H A P T E R

5


Obj. 5 1–9, 13–17

Obj. 10 17

2 N D P R I N T

478 Chapter 6 Polynomial Functions

Add or subtract. Write your answer in standard form.

1. (3x2 - x + 1) + (x) 2. (6x3 - 3x + 2) - (7x3 + 3x + 7) 3. (y2 + 3 y2 + 2 )+ (y4 + y 3 - y2 + 5) 4. (4x4 + x2) - (x3 - x2 - 1)

5. The cost of producing x units of a product can be modeled by C(x) = 1__10

x3 - x2 + 25. Evaluate C(x) for x = 15, and describe what the value represents.

Find each product.

6. xy (2x4 y + x2 y2 - 3x y 3) 7. (t + 3)(2t2 - t + 3) 8. (x + 5) 3 9. (2y + 3)4

Divide.

10. (5x2 - 6x - 8) ÷ (x - 2) 11. (2x3 - 7x2 + 9x - 4) ÷ (2x - 1)

12. Use synthetic substitution to evaluate x4 + 3 x3 - x2 + 2x - 6 for x = 3.

Factor each expression.

13. -2x2 - 6x + 56 14. m5 + m4 - 625m - 625 15. 4 x3 - 32

16. Identify the roots of the equation 2 x4 - 9x3 + 7 x2 + 2x - 2 = 0. State the multiplicity of each root.

17. Write the simplest polynomial function with roots of 1, 4, and -5.

Identify whether the function graphed has an odd or even degree and a positive or negative leading coefficient.

18. 19. 20.

Let f (x) = 12 x3+ 4. Graph f (x) and g (x) on the same coordinate plane. Describe

g (x) as a transformation of f (x).

21. g (x) = f (-x) 22. g (x) = 1_2

f (x) 23. g (x) = -f (x) + 3

24. The table shows the number of bracelets Carly can make over time. Write a polynomial function for the data.

Time (h) 1 2 3 4 5 6

Bracelets 3 5 11 21 35 53

25. The table shows the number of sandwiches sold each day at a deli over 5 days. Write a polynomial function for the data.

Day 1 2 3 4 5

Sandwiches 57 72 101 89 66

478

3x2+ 1

3. y 4 + y3+ 3 y2

+ 7

- x3- 6x - 5

4x4- x3

+ 2 x2+ 1

2x5y2+ x3y3

- 3x2y4 2 t3+ 5 t2

+ 9

x3+ 15 x2

+ 75x + 125 16 y4+ 96 y3

+ 216 y2+ 216y + 81

5x + 4x2

- 3x + 3 + -1_

2x - 1153

-2(x + 7)(x - 4)

(m + 1)(m + 5)(m - 5)(m2+ 25) 4(x - 2)(x2

+ 2x + 4)

1, - 1_2

, 2 + √ � 2 , 2 - √ � 2 , all with multiplicity 1 x3

- 21x + 20

odd; negative odd; positive even; positive

C(15) = 137.50; the cost of manufacturing 15 units is $137.50.

f (x) = 2 x2- 4x + 5

f (x) = 3.54 x4- 44.58x3

+ 185.96x2- 283.92x + 196

478 Chapter 6


Online Edition


Chapter 6 Tests




IDEA Works! CD-ROM


Answers 21. reflection

across y-axis

22. vertical com-pression by 1__

2

23. reflectionacross x-axisand shift 3 units up

C H A P T E R

6


Obj. 2 1–7, 10, 11, 13–15

2 N D P R I N T

pre ap/tag algebra ii final exam revie fall final review solutions.pdfthese review problems are...

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