university of vermont - kent state university

COLLEGE ALGEBRA IN CONTEXT

WITH APPLICATIONS

FOR THE MANAGERIAL, LIFE,AND SOCIAL SCIENCES

SECOND EDITION

Ronald J. HarshbargerUniversity of South Carolina–Beaufort

Lisa S. YoccoGeorgia Southern University

INSTRUCTOR’S

TESTING MANUAL

KARLA KARSTENSUniversity of Vermont

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Copyright 2007 Pearson Education, publishing as Pearson Addison-Wesley.

Reproduced by Pearson Addison-Wesley from electronic files supplied by the author.

Copyright © 2007 Pearson Education, Inc.Publishing as Pearson Addison-Wesley, 75 Arlington Street, Boston, MA 02116.

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ISBN 0-321-36981-5

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This work is protected by United States copyright laws and is provided solelyfor the use of instructors in teaching their courses and assessing student

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TABLE OF CONTENTS

Chapter 1 Functions, Graphs, and Models; Linear Functions ……………………………...1 Chapter 2 Quadratic and Other NonLinear Functions ..…………………………………….7 Chapter 3 Exponential and Logarithmic Functions ……………………………………….13 Chapter 4 Higher-Degree Polynomial and Rational Functions …………………………...19 Chapter 5 Systems of Equations and Matrices ……………………………………………25 Chapter 6 Special Topics: Systems of Inequalities and Linear Programming;

Sequences and Series; Preparing for Calculus …………………………………31 Answers …………………………………………………………………...………………….. 37


ACKNOWLEDGEMENTS I would like to express my gratitude to Larry Kost, Helen Read, and Joe Kudrle for their technical assistance in creating this manual.


Chapter 1 Test Form A 1 1. Determine the domain and range for each function. a. b. 2

1 8y x= −

c. 1

( ) 63

f x x= +

2. Graph each function with a graphing calculator using the standard viewing window. Determine the x-intercept(s) and y-intercept of each function, if they exist. a. 2 4y x= −

b. 3

1y

x=

+

c. 3 22 6y x x= − 3. Find the slope and y-intercept for each linear equation. a. 6 12y x= − b. 5 2 15x y− =

c. 12

y x=

4. Find the slope of a line through the given points. a. (-3, 5) and (6, 2) b. (2, 4) and (-7, 4) c. (0, 6) and(-2, -1) 5. The membership of a popular club from 1990 to 2000 is given by the function

( ) 22 18N x x= + people, x years after the club was founded in 1990. a. What is the membership of the club in 1995? b. Find and interpret the y-intercept of the function. c. Find the rate of change in the number of members in the club. 6. Write the equation of a line with the given characteristics: a. slope of 2 and a y-intercept of 4 b. slope of -3 and passing through the point (6, 1) c. undefined slope and passing through the point (2, 5)

x 4 2 1 3 6 ( )f x 7 5 2 0 3


2 Chapter 1 Test Form A 7. Write the equation of a line through the point (1, 4) with the given characteristics: a. parallel to 2 6x y+ =

b. perpendicular to 1

24

y x= −

c. perpendicular to the y-axis

8. Find ( ) ( )f x h f x

h+ −

for ( ) 2 3f x x= − .

9. The table shows the number of books checked out from a village library by local residents from 1995 through 1999.

Year 1995 1996 1997 1998 1999 Books (in thousands) 412 476 538 601 664

a. Explain why a linear equation is a reasonable model for this data. b. Find the linear model that is the best fit for this data, with x equal to the number of years after 1995. c. Use the unrounded model to predict the number of books that will be checked out of the library in 2004. 10. Solve the systems of linear equations, if possible.

a. 2 114 3 7

x y

x y

+ =�� − =�

b. 5 9

3 7y x

x y

= +�� − = −�

c. 2 8

4 2 6y x

x y

= −�� − =�

11. The cost to create a wind chime is given by ( ) 14.5 304.5C x x= + dollars, when x wind chimes are made. The wind chimes sell for $50 each. Find the number of units that gives break-even for the wind chimes. 12. A job candidate is given the choice of two positions, one paying $4,200 per month and the other paying $2,600 per month plus a 6% commission on all sales made during the month. What amount must the employee sell in a month for the second position to be more profitable?


Chapter 1 Test Form B 3 1. Determine the domain and range for each function. a. b. 2

1 4y x= −

c. 5

( ) 108

f x x= −

2. Graph each function with a graphing calculator using the standard viewing window. Determine the x-intercept(s) and y-intercept of each function, if they exist. a. 5 1y x= −

b. 2

1y

x=

−

c. 3 22 6y x x= + 3. Find the slope and y-intercept for each linear equation. a. 4 6y x= + b. 3 2 6x y+ = c. 4y = − 4. Find the slope of a line through the given points. a. (-3, 6) and (6, 1) b. (2, 9) and (-7, 5) c. (0, 6) and(-2, -6) 5. The absorption of a certain drug into the body is given by ( ) 0.084 0.42A x x= − + grams, x hours after the drug was taken. a. How much of the drug is absorbed into the body 3 hours after it was taken? b. Find and interpret the y-intercept of the function. c. What is the rate of change in the absorption of the drug into the body? 6. Write the equation of a line with the given characteristics:

a. slope of 23

and a y-intercept of -3

b. slope of -4 and passing through the point (2, 1) c. undefined slope and passing through the point (-1, 1)

x -4 -2 1 3 6 ( )f x -1 1 4 7 9


4 Chapter 1 Test Form B 7. Write the equation of a line through the point (3, 4) with the given characteristics: a. parallel to 2 6x y+ =


43

y x= +


8. Find ( ) ( )f x h f x

h+ −

for ( ) 3 1f x x= − .

9. The table shows the dividends per share of HWK, Inc. stock from 1990 through 1998.

Year 1990 1991 1992 1993 1994 1995 1996 1997 1998 Dividends (in dollars) 0.16 0.19 0.24 0.27 0.31 0.34 0.38 0.41 0.45

a. Explain why a linear equation is a reasonable model for this data. b. Find the linear model that is the best fit for this data, with x equal to the number of years after 1990. c. Use the unrounded model to predict the dividends per share of HWK, Inc. for 2005. 10. Solve the systems of linear equations, if possible.

a. 3 10

3 10x y

x y

− = −�� + =�

b. 2 6

4 2y x

x y

= +�� − = −�

c. 4

2 2 5y x

x y

= +�� − =�

11. The cost to create a bracelet is given by ( ) 3.5 20C x x= + dollars, when x bracelets are made. The bracelets sell for $11 each. Find the number of units that gives break-even for the bracelets. 12. If Torrey has a course average score between 90 and 100, he will earn a grade of A in his algebra course. Suppose he has 4 exam scores of 88, 93, 85 and 92 and that the final exam score has twice the weight of the other four exams. What range of scores on the final exam will result in Torrey earning a grade of A?


Chapter 1 Test Form C 5 1. Determine the domain and range for each function. a. b. 2

1 2y x= +

c. 3

( ) 64

f x x= −

2. Graph each function with a graphing calculator using the standard viewing window. Determine the x-intercept(s) and y-intercept of each function, if they exist. a. 4y x= −

b. 4

2 1y

x=

+

c. 3 26y x x= + 3. Find the slope and y-intercept for each linear equation. a. 3 2y x= − b. 5 3 15x y+ = c. 6y = 4. Find the slope of a line through the given points. a. (-3, 2) and (6, 1) b. (2, 5) and (-3, 5) c. (0, 4) and(-2, -6) 5. Weekly sales of a new book at a book store are given by ( ) 51 32S x x= + books, x weeks after publication. a. How many books were sold 5 weeks after publication? b. Find and interpret the y-intercept of the function. c. Find the rate of change in the number of books sold per week. 6. Write the equation of a line with the given characteristics:

a. slope of 23

and a y-intercept of 5

b. slope of -1 and passing through the point (2, 1) c. undefined slope and passing through the point (5, 1)

x -2 0 2 4 6 ( )f x -3 1 5 9 13


6 Chapter 1 Test Form C 7. Write the equation of a line through the point (5, -2) with the given characteristics: a. parallel to 2 6x y+ =


43

y x= +


8. Find ( ) ( )f x h f x

h+ −

for ( ) 4 3f x x= + .

9. The table shows the dividends per share of KSBW, Inc. stock from 1990 to 1998.

Year 1990 1991 1992 1993 1994 1995 1997 1998 1999 Dividends (in dollars) 0.30 0.34 0.39 0.43 0.47 0.51 0.56 0.61 0.66

a. Explain why a linear equation is a reasonable model for this data. b. Find the linear model that is the best fit for this data, with x equal to the number of years after 1990. c. Use the unrounded model to predict the dividends per share of KSBW, Inc. for 2005. 10. Solve the systems of linear equations, if possible.

a. 2 2

4 26x y

x y

+ = −�� − =�

b. 5 8

2 3 11y x

x y

= +�� − = −�

c. 4

3 3 5y x

x y

= +�� − =�

11. The cost to create a cutting board is given by ( ) 15.4 350C x x= + dollars, for x cutting boards made. The cutting boards sell for $25 each. Find the number of units that gives break-even for the cutting board. 12. If Kenny has a course average score between 80 and 89, he will earn a grade of B in his algebra course. Suppose he has 4 exam scores of 76, 81, 82, and 77, and that the final exam score has twice the weight of the other three exams. What range of scores on the final exam will result in Kenny earning a grade of B?


Chapter 2 Test Form A 7 1. For each of the following functions, find the value of (2)f , if possible.

a. 4

( ) 84

f xx

= +−

b. 3 4, 2

( )6, 2

x xf x

x x

− <�= � + ≥�

c. 2( ) 3( 3) 6f x x= − + d. ( ) 5 4f x x= − +

2. Find the coordinates of the vertex of the graph for each of the following. a. 2( ) 2( 5) 1f x x= − − +

b. 2( ) 6 7f x x x= + + 3. The graph of 2( ) ( 1) 3f x x= − − is shown below.

a. Decide whether the function is even, odd, or neither. b. Describe the increasing and decreasing behavior of the function. c. Describe the concavity of the function. d. What is the domain and range of this function? 4. Find the x-intercepts of each function. a. 2( ) 2 15f x x x= − −

b. 2( ) 2 6 1f x x x= − + 5. Given 2( ) 2f x x= − and 3( ) 2 5g x x= − , find each of the following. a. ( )(2)f g+ b. ( )( 3)f g− −

c. ( )( 2)fg − d. (4)fg

� ��

6. Given 2( ) ( 1)f x x= + and 4

( )g xx

= , find each of the following.

a. ( )( 3)f g −� b. ( )( )g f x� 7. Find the inverse of 3( ) ( 4)f x x= + . 8. Solve 2 1 3x − ≤ .

9. Solve 24 7 1x x− = − .


8 Chapter 2 Test Form A 10. The profit from making and selling x units of a product is given by 2( ) 2 15 600f x x x= − + dollars. How many units should be produced and sold in order to make a profit of $1475? 11. The cost of a movie ticket, in dollars, depends on x, the age of the person attending the movie, and is described below by the piecewise function.

5, 13( ) 7,13 55

6, 55

x

C x x

x

<�= ≤ <� ≥�

Find (35)C and interpret its meaning in the context of the problem. 12. The population of a certain city is given in the following table. Year 1920 1930 1940 1950 1960 1970 1980 Population 796,800 900,400 920,250 914,760 874,030 750,870 573,128 a. Using an input equal to the number of years after 1920, find a quadratic function to model this data. b. Use the unrounded function to estimate the population in 1955. c. If the population continues according to the model, when will the population of the city be 500,000 people?


Chapter 2 Test Form B 9 1. For each of the following functions, find the value of (5)f , if possible.

a. 4

( ) 84

f xx

= +−

b. 3 4, 2

( )6, 2

x xf x

x x

− <�= � + ≥�

c. 2( ) 3( 3) 6f x x= − + d. ( ) 5 4f x x= − +

2. Find the coordinates of the vertex of the graph for each of the following. a. 2( ) 6( 4) 2f x x= + −

b. 2( ) 4 7f x x x= − + 3. The graph of 2( ) 8 2f x x= − is shown below.

a. Decide whether the function is even, odd, or neither. b. Describe the increasing and decreasing behavior of the function. c. Describe the concavity of the function. d. What is the domain and range of this function? 4. Find the x-intercepts of each function. a. 2( ) 4 21f x x x= + −

b. 2( ) 3 6 1f x x x= + + 5. Given 2( ) 1 4f x x= − and 3( ) 6g x x= − , find each of the following. a. ( )(2)f g+ b. ( )( 3)f g− −

c. ( )( 2)fg − d. (4)fg

� ��

6. Given 2( ) ( 2)f x x= − and 2

( )1

g xx

=+

, find each of the following.

a. ( )( 3)f g −� b. ( )( )g f x�

7. Find the inverse of 3( ) 5f x x= − . 8. Solve 4 1 6x + ≤ .

9. Solve 22 1 2x x− = + .


10 Chapter 2 Test Form B 10. The profit from making and selling x units of a product is given by 2( ) 2 12 800f x x x= − + dollars. How many units should be produced and sold in order to make a profit of $1760? 11. The cost of a birthday party, in dollars, depends on x, the number of people attending the party, and is described below by the piecewise function.

75, 10( )

75 6( 10), 10x

C xx x

≤�= � + − >�

Find (12)C and interpret its meaning in the context of the problem. 12. The population of a certain city is given in the following table. Year 1920 1930 1940 1950 1960 1970 1980 Population 381,768 560,660 796,841 900,429 925,765 914,808 876,050 a. Using an input equal to the number of years after 1920, find a quadratic function to model this data. b. Use the unrounded function to estimate the population in 1955. c. If the population continues according to the model, when will the population of the city drop to 750,000 people again?


Chapter 2 Test Form C 11 1. For each of the following functions, find the value of ( 4)f − , if possible.

a. 4

( ) 28

f xx

= −−

b. 2 4, 2

( )3 6, 2

x xf x

x x

− <�= � + ≥�

c. 2( ) ( 5) 2f x x= + − d. ( ) 7 5f x x= − +

2. Find the coordinates of the vertex of the graph for each of the following. a. 2( ) 5( 2) 1f x x= + +

b. 2( ) 5 2f x x x= + + 3. The graph of 2( ) ( 4)f x x= + is shown below.

a. Decide whether the function is even, odd, or neither. b. Describe the increasing and decreasing behavior of the function. c. Describe the concavity of the function. d. What is the domain and range of this function? 4. Find the x-intercepts of each function. a. 2( ) 2 7 4f x x x= + −

b. 2( ) 6 1f x x x= − + 5. Given 2( ) 1 3f x x= − and 3( ) 2g x x= + , find each of the following. a. ( )(2)f g+ b. ( )( 3)f g− −

c. ( )( 2)fg − d. (4)fg

� ��

6. Given 2( ) 3( 1)f x x= − and 3

( )2

g xx

= , find each of the following.

a. ( )( 3)f g −� b. ( )( )g f x� 7. Find the inverse of ( ) 6 7f x x= − . 8. Solve 2 1 6x + ≤ .

9. Solve 24 7 1x x− = + .


12 Chapter 2 Test Form C 10. The profit from making and selling x units of a product is given by 2( ) 2 10 600f x x x= − + dollars. How many units should be produced and sold in order to make a profit of $2700? 11. The cost of gas, in dollars, used by a household in Hennepin County depends on x, the number of therms used each month, and is described below by the piecewise function.

1.5 , 10( ) 1.7 ,10 50

2.2 , 50

x x

C x x x

x x

<�= ≤ <� ≥�

Find (50)C and interpret its meaning in the context of the problem. 12. The population of a certain city is given in the following table. Year 1920 1930 1940 1950 1960 1970 1980 Population 600,400 660,030 700,700 675,450 590,000 440,765 330,125 a. Using an input equal to the number of years after 1920, find a quadratic function to model this data. b. Use the unrounded function to estimate the population in 1955. c. If the population continues according to the model, when will the population of the city be 250,000 people?


Chapter 3 Test Form A 13 1. Use the properties of logarithms to evaluate the expressions. a. 6log10 b. 3ln e c. log510 d. ln 0.4e 2. Rewrite each expression as the sum, difference, or product of logarithms and simplify if possible.

a. 3

1log

( 4)x� �� +�

b. 3ln 4 2x −

3. Rewrite each expression as a single logarithm.

a. 2ln 3lnx y− b. 1

3(ln ln ) ln2

x y z+ −

In Problems 4 – 8, solve the equation. 4. 5log 3x = 5. 3ln 5x = 6. 36 10x− = 7. 48(5 ) 10x = 8. ln(2 1) 9x + = 9. The amount of polonium-12 present at time t is given by 0.00495( ) 70A t e−= grams, where t is the time in days that an isotope decays. a. How many grams remain after 100 days? b. How many days will it take for only 2 grams of polonium-12 to remain? 10. The sales for a furniture manufacturer is given in the table below. Year 1974 1978 1982 1986 1990 1994 1998 2002 Sales (in millions) 23 38.4 64 107 179 299 499 833 a. Find an exponential function that models the data, using an input of the number of years after 1974. b. Use the model to estimate furniture sales for 2006. 11. Suppose that $4,200 is invested at 6% for 10 years. Find the total amount present at the end of this time period if the interest is compounded (a) monthly and (b) continuously. 12. The number of frogs in a lake is given by ( ) 80 ktP t e= , where t = 0 represents the year 1980. In 1985 the number of frogs in the lake is 100. a. Find the value of k. b. Use the result from part (a) to predict the number of frogs in 1990.


Chapter 3 Test Form B 15 1. Use the properties of logarithms to evaluate the expressions. a. 3log10 b. 2ln e− c. 6log 76 d. ln3.2e 2. Rewrite each expression as the sum, difference, or product of logarithms and simplify if possible.

a. 4log(6 5)x + b. 3

1ln

x� ��


a. 4log (2 log 3log )x y z− + b. 1

(ln ln 3)2

x −

In Problems 4 – 8, solve the equation. 4. 2log 5x = 5. ln 2 5x = 6. 26 12x = 7. 12(3 ) 10x+ = 8. ln( 1) 4x + = 9. The amount of a drug present in the blood plasma of a patient is given by 0.0315( ) 15 hA h e−= µ g/mL, h hours after the drug reaches its peak concentration. a. What is the concentration of the drug in the blood plasma 8 hours after it reaches peak concentration? b. How many hours after peak concentration will it take for only 10 µ g/ml to remain? 10. The population of a country is given in the table below. Year 1920 1930 1940 1950 1960 1970 1980 1990 Population (in millions) 14 16.5 19.6 25.8 34.9 48.2 66.8 81.2 a. Find an exponential function that models the data, using an input of the number of years after 1920. b. Use the model to estimate the population for 2010. 11. Suppose that $6,800 is invested at 3% for 25 years. Find the total amount present at the end of this time period if the interest is compounded (a) monthly and (b) continuously. 12. The number of rabbits in a field is given by ( ) 15 ktP t e= , where t = 0 represents the year 1990. In 1992 the number of rabbits in the field is 22. a. Find the value of k. b. Use the result from part (a) to predict the number of rabbits in the field in 1996.


Chapter 3 Test Form C 17 1. Use the properties of logarithms to evaluate the expressions. a. 5log10 b. ln e c. 4log 34 d. 2ln3e 2. Rewrite each expression as the sum, difference, or product of logarithms and simplify if possible.

a. 1

logy

� ��

b. 3ln (2 1)x y +


a. ln 4(ln ln )x y z+ − b. 1

(ln 2ln ) ln3

x y z+ −

In Problems 4 – 8, solve the equation.

4. 4log 2x = 5. 1

ln 52

x =

6. 32 4x+ = 7. 34 10x =

8. ln 32x� �=� �

�

9. A bicyclist begins coasting on flat ground at 20 miles per hour. The cyclist’s speed is given by

1.55( ) 20 tv t e−= miles per hour, where t is the number of minutes coasting. a. What is the cyclist’s speed after coasting for 2 minutes? b. When is the cyclist’s speed 5 miles per hour? 10. The sales for a clothing company are given in the table below. Year 1974 1976 1978 1980 1982 1984 1986 1988 Sales (in millions) 8 12.8 20.5 32.8 52.5 84 134.4 215 a. Find an exponential function that models the data, using an input of the number of years after 1974. b. Use the model to estimate sales for 1994. 11. Suppose that $8600 is invested at 6% for 8 years. Find the total amount present at the end of this time period if the interest is compounded (a) monthly and (b) continuously. 12. The number of turtles in a lake is given by ( ) 12 ktP t e= , where t = 0 represents the year 2000. In 2005 the number of turtles in the lake is 30. a. Find the value of k. b. Use the result from part (a) to predict the number of frogs in 2010.


Chapter 4 Test Form A 19 1. Consider the function 4 3( ) 5 6 2 7f x x x x= − − + . a. What is the degree of the polynomial? b. Describe the end behavior of the function.

2. Graph 3 212 3 1

3y x x x= + + − using a window that shows a local maximum and local minimum.

a. Where does the local maximum occur? b. Where does the local minimum occur? 3. Solve 4 24 36 0x x− = . 4. Solve 4 3 23 18 0x x x− − = . 5. Use factoring by grouping to solve 3 24 9 20 45 0x x x+ − − = . 6. If x = 2 is a solution of 3 27 2 40 0x x x+ + − = , find the remaining solutions. 7. Use the root method to solve 33( 4) 81x − = .

8. Consider the function 4 1

5x

yx

+=−

.

a. Find the x-intercept and y-intercept of the function. b. Find any horizontal asymptotes that exist. c. Find any vertical asymptotes that exist. 9. Solve 4 217 16 0x x− + = . 10. Find the exact solutions to 3 20 4 4 16x x x= − + − in the complex number system.

11. Solve 2

23

xx

− ≥+

.

12. The average cost for a certain product is given by 21000 20 0.1

( )x x

C xx

+ += , where x is the

number of hundreds of units produced. Find the average cost per unit when 3000 units are produced.


Chapter 4 Test Form B 21 1. Consider the function 3 2( ) 2 6 3 8f x x x x= − − + − . a. What is the degree of the polynomial? b. Describe the end behavior of the function.

2. Graph 3 218 2

3y x x x= − − + using a window that shows a local maximum and local minimum.

a. Where does the local maximum occur? b. Where does the local minimum occur? 3. Solve 4 29 0x x− = . 4. Solve 4 3 22 5 3 0x x x− − = . 5. Use factoring by grouping to solve 3 23 2 15 10 0x x x− + − = . 6. If x = 3 is a solution of 3 28 9 18 0x x x− + + = , find the remaining solutions. 7. Use the root method to solve 32( 1) 16x + = .


3x

yx

+=−

.

a. Find the x-intercept and y-intercept of the function. b. Find any horizontal asymptotes that exist. c. Find any vertical asymptotes that exist. 9. Solve 4 24 17 4 0x x− + = . 10. Find the exact solutions to 3 20 4 5 6x x x= + + + in the complex number system.

11. Solve 4

41

xx

− ≥+

.


( )x x

C xx

+ += , where x is the number

of hundreds of units produced. Find the average cost per unit when 4000 units are produced.


Chapter 4 Test Form C 23 1. Consider the function 2 6 4( ) 5 6 2 7f x x x x x= − − + . a. What is the degree of the polynomial? b. Describe the end behavior of the function. 2. Graph 3 22 6 1y x x= + + using a window that shows a local maximum and local minimum. a. Where does the local maximum occur? b. Where does the local minimum occur? 3. Solve 4 23 3 0x x− = . 4. Solve 4 3 25 14 0x x x+ − = . 5. Use factoring by grouping to solve 3 22 8 4 0x x x− + − = . 6. If x = 1 is a solution of 3 22 11 12 0x x x− − + = , find the remaining solutions. 7. Use the root method to solve 32( 5) 128x + = .


4x

yx

+=−

.

a. Find the x-intercept and y-intercept of the function. b. Find any horizontal asymptotes that exist. c. Find any vertical asymptotes that exist. 9. Solve 4 29 37 4 0x x− + = . 10. Find the exact solutions to 3 20 2 7 3 4x x x= − − − in the complex number system.

11. Solve 5

52

xx

− ≥+

.


( )x x

C xx

+ += , where x is the

number of hundreds of units produced. Find the average cost per unit when 5000 units are produced.


Chapter 5 Test Form A 25

1. Write the system

3 4 2 42 5 2

3 12

x y z

x y z

x y z

+ − =� − + = −� − − = −�

as an augmented matrix.

2. The matrix associated with the solution to a system of linear equations in x, y, and z is given. Write the solution to the system, if it exists.

a.

1 0 0 60 1 0 20 0 1 5

� � �− � ��

b.

1 0 0 60 2 0 80 0 3 6

� � � � ��

c.

1 0 2 60 1 1 20 0 0 0

� � �− � ��

3. Solve the system

2 72 8

2 7

x y z

x y z

x y z

+ + =� − + =� + − = −�

algebraically, if a solution exists.

4. Solve the system

2 13 2

2 2 4 7

x y z

x y z

x y z

− + = −� + − =� − + =�


5. A theater owner wants to divide a 1500 seat theater into three sections, with tickets costing $10, $20, and $50, depending on the section. He wants to have twice as many $10 tickets as the sum of the other tickets, and he wants to earn $21,000 from a full house. How many of each type of ticket should he sell?

6. Given 2 11 3

A� �

= �−� �, find 2A .

7. Given

4 12 03 7

A

−� � �= � ��

and

5 12 4

3 0B

� � �= − � ��

, find each of the following, if possible.

a. A B+ b. 3 2A B− c. AB

8. Given

5 13 20 3

A

−� � �= � ��

and 5 1

2 4B

� �= �−� �

, find AB .

9. Show that 1 51 4� � ��

and 4 5

1 1−� � �−� �

are inverses.


26 Chapter 5 Test Form A

10. Given 2 3

3 4A

−� �= �−� �

.

a. Find 1A− .

b. Use the inverse from part (a) to solve the system of linear equations 2 3 7

3 4 11x y

x y

− + = −�� − =�

.

11. Youngclaus Trucking Company has an order for three product; A, B, and C, for delivery. The following table gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of each of the products. If one of the company’s trucks can carry 4550 cubic feet and 6,060 pounds, and is insured to carry $25,300, how many units of each product can be carried on the truck?

12. Solve the nonlinear system 2 4

2 1x y x

x y

� + =�

− = −�.

Product A Product B Product C Unit Volume (cubic feet)

25 30 40

Weight (pounds)

30 36 60

Insurance Value (dollars)

150 180 200


Chapter 5 Test Form B 27

1. Write the system

2 6 53 2 7

4 8

x y z

x y z

x y z

+ − =� − + =� − − =�



a.

1 0 0 80 1 0 30 0 1 2

� � � � �− ��

b.

1 0 0 60 3 0 60 0 4 8

� � �− � ��

c.

1 0 1 40 1 1 30 0 0 1

� � � � ��

3. Solve the system

2 53 16

2 9

x y z

x y z

x y z

+ + =� − + =� + − =�


4. Solve the system

2 83 11

2 2 4 18

x y z

x y z

x y z

− + =� + − = −� − + =�


5. A trust account manager has $80,000 to invest in three different accounts. The accounts pay 85, 10%, and 14%, respectively, and the goal is to earn $9,200 with the amount invested at 14% equal to the sum of the other two investments. How much should the account manager invest in each account?

6. Given 4 23 1

A� �

= �− −� �, find 2A .

7. Given

4 12 03 7

A

−� � �= � ��

and

5 12 4

3 0B

� � �= − � ��


a. 2 4A B+ b. 3B A− c. BA

8. Given

1 12 40 6

A

−� � �= � ��

and 3 0

2 6B

� �= �−� �

, find AB .

9. Show that 4 13 1� � ��

and 1 13 4

−� � �−� �

are inverses.


28 Chapter 5 Test Form B

10. Given 6 52 2

A� �

= ��

.

a. Find 1A− .

b. Use the inverse from part (a) to solve the system of linear equations 6 5 92 2 4

x y

x y

+ =�� + =�

.

11. Mitchell Trucking Company has an order for three product; A, B, and C, for delivery. The following table gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of each of the products. If one of the company’s trucks can carry 4500 cubic feet and 5,880 pounds, and is insured to carry $25,400, how many units of each product can be carried on the truck?

12. Solve the nonlinear system 2 5

2 4x y x

x y

� + =�

− =�.


25 30 40

Weight (pounds)

30 36 60


150 180 200


Chapter 5 Test Form C 29

1. Write the system

4 3 22 4 7 64 2 2

x y z

x y z

x y z

+ − =� − + =� − − = −�



a.

1 0 0 50 1 0 10 0 1 6

� � �− � �− ��

b.

1 0 0 60 4 0 80 0 2 6

� � � � ��

c.

1 0 1 60 1 2 20 0 0 3

� � �− � ��

3. Solve the system

2 11

3

x y z

x y z

x y z

+ + =� − + = −� + − =�


4. Solve the system

2 13 2

2 2 4 2

x y z

x y z

x y z

− + = −� + − =� − + = −�


5. A theater owner wants to divide a 1800 seat theater into three sections, with tickets costing $10, $20, and $40, depending on the section. He wants to have twice as many $10 tickets as the sum of the other tickets, and he wants to earn $28,000 from a full house. How many of each type of ticket should he sell?

6. Given 4 31 5

A−� �

= �−� �, find 2A .

7. Given

1 16 53 2

A

−� � �= � �−� �

and

5 12 4

3 0B

� � �= − � ��


a. A B+ b. 3 2A B− c. AB

8. Given

4 12 2

1 3A

−� � �= − � ��

and 3 1

2 4B

� �= �−� �

, find AB .

9. Show that 3 71 2� � ��

and 2 7

1 3−� � �−� �

are inverses.


30 Chapter 5 Test Form C

10. Given 4 13 1

A� �

= ��

.

a. Find 1A− .

b. Use the inverse from part (a) to solve the system of linear equations 4 103 7

x y

x y

+ =�� + =�

.

11. Corey Trucking Company has an order for three product; A, B, and C, for delivery. The following table gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of each of the products. If one of the company’s trucks can carry 3220 cubic feet and 4,100 pounds, and is insured to carry $19,200, how many units of each product can be carried on the truck?

12. Solve the nonlinear system 2

4 10x y x

x y

� − =�

+ =�.


20 35 40

Weight (pounds)

30 40 50


160 180 200


Chapter 6 Test Form A 31 1. Sketch the graph of the inequality 2 4x y− ≥ − . 2. Graph the following system of inequalities and identify the corners of the solution region.

2 82

2 4

x y

x y

x y

+ ≤�− + ≥ −� + ≥�

3. Graph the solution of the nonlinear inequalities 2

2

4 20

10

x x y

x y x

� − + ≤�

+ ≤�.

4. The corner points of a certain feasibility region are (0, 0), (0, 5), (3, 2) and (4, 0). Which corner point maximizes the value of 2 4C x y= + ? 5. Find the maximum value of 4 3f x y= + and the values of x and y that give the value, subject to the

constraints

2 129

0, 0

x y

x y

x y

+ ≤� + ≤� ≥ ≥�

.

6. Determine whether each of the following sequences are arithmetic or geometric.

a. 4 8 16

3, 2, , , ,...3 9 27

b. 8,3, 2, 7, 12,...− − − 7. Find the 12th term of the geometric sequence 6, 12, 24, 48,...− −

8. A ball is dropped from a height of 80 feet and rebounds 35

of the height from which it falls every time

it hits the ground. How high will the ball bounce after it hits the ground the fourth time? 9. Find the sum of the first 50 terms of the arithmetic sequence 30, 35, 40, 45, 50, . . .

10. Find the sum of the geometric series 1

(0.3)i

i

∞

=� .

11. Write 4 3 4

3 1 42

yx x x

= − + with each term in the form ncx .

12. Find where '( ) 0f x = if 3 5 4 4'( ) (2 1) ( 6) (2 1) ( 6)f x x x x x= + − + + − .


Chapter 6 Test Form B 33 1. Sketch the graph of the inequality 3 6x y+ ≥ − . 2. Graph the following system of inequalities and identify the corners of the solution region.

42 4

0

x y

x y

y

+ ≤� − ≥ −� ≥�


2

8 28

( 4) 20

x x y

x y

� − + ≤�

− ≤ −�.

4. The corner points of a certain feasibility region are (0, 0), (0, 5), (2, 4) and (4, 0). Which corner point maximizes the value of 3 4C x y= + ? 5. Find the maximum value of 3 2f x y= + and the values of x and y that give the value, subject to the

constraints

2 64

0, 0

x y

x y

x y

+ ≤� + ≤� ≥ ≥�

.


a. 3 2 7 12

2, , , , , ...4 4 4 4

− − −

b. 2, 3, 4.5 ,6.75 ,10.125, ... 7. Find the 12th term of the geometric sequence 2, 6,18, 54, ...− −


of the height from which it falls every

time it hits the ground. How high will the ball bounce after it hits the ground the fourth time? 9. Find the sum of the first 50 terms of the arithmetic sequence 15, 18, 21, 24, 27, . . .


25

i

i

∞

=

� ��

� .

11. Write 5 3 3

2 1 53

yx x x


12. Find where '( ) 0f x = if 2 5 3 4'( ) (3 1) ( 2) (3 1) ( 2)f x x x x x= − + + − + .


Chapter 6 Test Form C 35 1. Sketch the graph of the inequality 2 3 6x y− ≥ . 2. Graph the following system of inequalities and identify the corners of the solution region.

6 182 3 12

0, 0

x y

x y

x y

+ ≤� + ≥� ≥ ≥�


2

2 8

( 4) 8

x x y

y x

� + + ≤�

≥ − −�.

4. The corner points of a certain feasibility region are (0, 0), (0, 5), (3, 2) and (4, 0). Which corner point maximizes the value of 3 2C x y= + ? 5. Find the maximum value of 21 40f x y= + and the values of x and y that give the value, subject to

the constraints

2 4 405 2 16

0, 0

x y

x y

x y

+ ≤� + ≤� ≥ ≥�

.


a. 9 27 81

4,3, , , ,...4 16 64

b. 5,2, 1, 4, 7,...− − −

7. Find the 12th term of the geometric sequence 3 3

6, 3, , ,...2 4

− −


of the height from which it falls every

time it hits the ground. How high will the ball bounce after it hits the ground the fourth time? 9. Find the sum of the first 40 terms of the arithmetic sequence 15, 27, 39, 51, 63, . . .


(0.7)i

i

∞

=� .

11. Write 7 6 3 2

2 3 42

yx x x


12. Find where '( ) 0f x = if 3 5 4 4'( ) ( 4) (3 2) ( 4) (3 2)f x x x x x= − − − − − .


Answers for Chapter 1 Test Form A 37 1. a. Domain = {4, 2, 1, 3, 6}, Range = {7, 5, 2, 0, 3} b. Domain = {all real numbers}, Range ={ : 8y y ≥ − } c. Domain = {all real numbers}, Range = {all real numbers} 2. a. x-intercept is 2, y-intercept is -4 b. no x-intercept, y-intercept is 3 c. x-intercepts are 0 and 3, y-intercept is 0 3. a. slope = 6, y-intercept is -12

b. slope = 52

, y-intercept is -7.5

c. slope = 12

, y-intercept is 0

4. a. -1/3 b. 0 c. 3.5 5. a. 128 members in 1995 b. The y-intercept is 18, which means the initial group membership was 18 members. c. The rate of change is 22 members per year. 6. a. 2 4y x= + b. 3 19y x= − + c. 2x = 7. a. 2 6y x= − + b. 4 8y x= − + c. 4y =

8. ( ) ( ) 2( ) 3 (2 3) 2

2f x h f x x h x h

h h h+ − + − − −= = =

9. a. The scatterplot appears linear. The first differences range from 62 to 64. b. ( ) 62.9 412.4N x x= + books, x years after 1995. c. 97.8 thousand books will be checked out in 2004. 10. a. (4, 3) b. (-1, 4) c. no solution 11. You would need to make and sell 9 wind chimes to break even. 12. The employee needs to sell more than $320,000 in order for the second position to be more profitable.


38 Answers for Chapter 1 Test Form B 1. a. Domain = {-4, -2, 1, 3, 6}, Range = {-1, 1, 4, 7, 9} b. Domain = {all real numbers}, Range ={ : 4y y ≤ } c. Domain = {all real numbers}, Range = {all real numbers}

2. a. x-intercept is 15

, y-intercept is -1

b. no x-intercept, y-intercept is -2 c. x-intercepts are 0 and -3, y-intercept is 0 3. a. slope = 4, y-intercept is 6

b. slope = 32

− , y-intercept is 3

c. slope = 0, y-intercept is -4 4. a. -5/9 b. 4/9 c. 6 5. a. 0.168 grams of the drug is absorbed into the body 3 hours after it is taken

b. The y-intercept is 0.42, which means that 0.42 grams of the drug are absorbed initially into the body.

c. The rate of change of the absorption of the drug into the body is -0.084 grams/hour.

6. a. 2

33

y x= −

b. 4 9y x= − + c. 1x = −

7. a. 1 112 2

y x= − +

b. 3 13y x= − + c. 4y =

8. ( ) ( ) 3( ) 1 (3 1) 3

3f x h f x x h x h

h h h+ − + − − −= = =

9. a. The scatterplot appears linear. The first differences range from 0.3 to 0.4. b. ( ) 0.036 0.161D x x= + dollars per share, x years after 1990. c. $ 0.70 dividends per share in 2005. 10. a. (-2, 4) b. (2, 10) c. no solution 11. You would need to make and sell 3 bracelets to break even. 12. Torrey needs to score 91 or better to get an A.


Answers for Chapter 1 Test Form C 39 1. a. Domain = {-2, 0, 2, 4, 6}, Range = {-3, 1, 5, 9, 13} b. Domain = {all real numbers}, Range ={ : 2y y ≥ } c. Domain = {all real numbers}, Range = {all real numbers} 2. a. x-intercept is 4, y-intercept is -4 b. no x-intercept, y-intercept is 4 c. x-intercepts are 0 and -6, y-intercept is 0 3. a. slope = 3, y-intercept is -2

b. slope = 53

− , y-intercept is 5

c. slope =0, y-intercept is 6 4. a. -1/9 b. 0 c. 5 5. a. 287 books sold 5 weeks after publication b. The y-intercept is 32, which is the number of books sold during the initial week of publication. c. The rate of change in the number of books sold is 51 books per week.

6. a. 2

53

y x= +

b. 3y x= − + c. 5x =

7. a. 1 12 2

y x= − +

b. 3 13y x= − + c. 2y = −

8. ( ) ( ) 4( ) 3 (4 3) 4

4f x h f x x h x h

h h h+ − + + − += = =

9. a. The scatterplot appears linear. The first differences range from 0.4 to 0.5. b. ( ) 0.045 0.296D x x= + dollars per share, x years after 1990. c. $ 0.96 dividends per share in 2005. 10. a. (2, -6) b. (-1, 3) c. no solution 11. You would need to make and sell 37 cutting boards to break even. 12. Kenny needs to score 82 or better to get a B.


40 Answers for Chapter 2 Test Form A 1. a. 6 b. 8 c. 9 d. 7 2. a. (5, 1) b. (-3, -2) 3. a. neither b. decreasing for 1x < , increasing for 1x > c. concave up d. Domain = {all real numbers}, Range = { : 3}y y ≥ − 4. a. (-3, 0) and (5, 0) b. (0.178, 0) and (2.823, 0)

5. a. 9 b. 52 c. 42 d. 14

123−

6. a. 19

b. 2

4( )( )

( 1)g f x

x=

+�

7. 3( ) 4f x x= − 8. 2 1x− ≤ ≤

9. 43

x =

10. 25 units 11. The cost of a movie ticket for a person who is 35 years old is $7. 12. a. 2( ) 260.981 2,029.229 797,003.810P t t t= − + + people, t years after 1920 b. 898,325 people c. early 1984


Answers for Chapter 2 Test Form B 41 1. a. 12 b. 11 c. 18 d. 4 2. a. (-4, -2) b. (2, 3) 3. a. even b. increasing for 0x < , decreasing for 0x > c. concave down d. Domain = {all real numbers}, Range = { : 8}y y ≤ 4. a. (7, 0) and (3, 0) b. (-1.816, 0) and (-0.184, 0)

5. a. -17 b. -68 c. -210 d. 6358

6. a. 9 b. 2

2( )( )

( 2)g f x

x=

−�

7. 3( ) 5f x x= +

8. 7 5

4 4x

− ≤ ≤

9. x = 5, 1 10. 20 units 11. The cost of a birthday party with 12 people will be $87. 12. a. 2( ) 295.291 26,003.407 368,964.738P t t t= − + + people, t years after 1920 b. 917,352 people c. middle of 1989


42 Answers for Chapter 2 Test Form C 1. a. -2 1/3 b. -12 c. -1 d. 16 2. a. (-2, 1) b. (-2.5,-4.25) 3. a. neither b. decreasing for 4x < − , increasing for 4x > − c. concave up d. Domain = {all real numbers}, Range = { : 0}y y ≤ 4. a. (-1/2, 0) and (4, 0) b. (0.172, 0) and (5.828, 0)

5. a. -1 b. -1 c. 66 d. 47

66−

6. a. 272

b. 2

1( )( )

2( 1)g f x

x=

−�

7. 1 7

( )6 6

f x x= +

8. 4 2x− ≤ ≤ 9. x = 2 10. 35 units 11. The cost of gas for a family that uses 50 therms in a month is $110. 12. a. 2( ) 228.723 8,866.054 602, 425.714P t t t= − + + people, t years after 1920 b. 632,551 people c. early 1983


Answers for Chapter 3 Test Form A 43 1. a. 6 b. 3 c. 5 d. 0.4 2. a. 3log( 4)x− +

b. 1

ln(4 2)3

x −

3. a. 2

3lnxy

b. 3( )

lnxy

z

4. x = 125 5. 3 5x =

6. ln10 3ln 6

4.285ln 6

x+= =

7. ln(1.25)

0.0354ln 5

x = =

8. 91( 1) 9051.042

2x e= − =

9. a. 42.670 grams b. 718 days 10. a. ( ) 22.982(1.137)tS t = millions, t years after 1974 b. 1391.89 million 11. a. $7641.47 b. $7652.90

12. a. ln(1.25)

5k =

b. 125 frogs


44 Answers for Chapter 3 Test Form B 1. a. 3 b. -2 c. 7 d. 3.2 2. a. 4log(6 5)x +

b. 1

ln3

x−

3. a. 4

2 3logx

y z

b. ln3x

4. x = 32

5. 5

2e

x =

6. ln12

0.6932ln 6

x = =

7. ln 5 ln 3

0.465ln 3

x−= =

8. 4( 1) 53.598x e= − = 9. a. 11.659 /g mLµ b. 12.872 hours 10. a. ( ) 12.588(1.027)tP t = millions, t years after 1920 b. 137.25 million people 11. a. $14,382.13 b. $14,395.60

12. a. 1 22

ln2 15

k � �= � ��

b. 48 rabbits


Answers for Chapter 3 Test Form C 45 1. a. 5 b. 1/2 c. 3 d. 9

2. a. 1

log2

y−

b. ln 3ln(2 1)x y+ +

3. a. 4

lny

xz

� ��

b. 23

lnxyz

4. x = 16 5. 10x e=

6. ln 4 3ln 2

1ln 2

x−= = −

7. ln10

0.5543ln 4

x = =

8. 32 40.171x e= = 9. a. 0.90 miles/ hour b. 0.894 minutes 10. a. ( ) 8(1.265)tS t = millions, t years after 1974 b. 881.52 million 11. a. $13,881.63 b. $13,898.24

12. a. ln(2.5)

5k =

b. 95 turtles


46 Answers for Chapter 4 Test Form A 1. a. 4th degree b. both ends open up 2. a. local maximum at (-3, -1) b. local minimum at (-1, -2 1/3)

3. 3 3

0, ,2 2

x−=

4. 0, 3,6x = −

5. 9

, 5, 54

x−= −

6. 5, 4x = − − 7. 7x = 8. a. x-intercept (-1/4, 0) and y-intercept (0, -1/5) b. y = 4 c. x = 5 9. 1,1, 4,4x = − − 10. 4, 2 , 2x i i= − 11. 8x > − 12. average cost per unit is 56.33


Answers for Chapter 4 Test Form B 47 1. a. 3rd degree b. opens down on right

2. a. local maximum at 1

( 2, 11 )3

−

b. local minimum at 2

(4, 24 )3

−

3. 0, 3,3x = −

4. 1

0,3,2

x = −

5. 2

, 5 , 53

x i i= −

6. 6, 1x = − 7. 1x = 8. a. x-intercept (-3, 0) and y-intercept (0, 2) b. y = 2 c. x = 3

9. 1 1

2, 2, ,2 2

x = − −

10. 1 7 1 7

3, ,2 2 2 2

x i i= − + − −

11. 2

23

x > −

12. average cost per unit is 34


48 Answers for Chapter 4 Test Form C 1. a. 6th degree b. both ends open down 2. a. local maximum at (-2, 9) b. local minimum at (0, 1) 3. 0, 1,1x = − 4. 0, 7, 2x = −

5. 2 2

4, ,2 2

x i i= −

6. 4, 3x = − 7. 1x = − 8. a. x-intercept (-4, 0) and y-intercept (0, -2) b. y = 2 c. x = 4

9. 1 1

, , 2, 23 3

x = − −

10. 1 7 1 7

4, ,4 4 4 4

x i i= − + − −

11. 3.75x > − 12. average cost per unit is 53


Answers for Chapter 5 Test Form A 49

1.

3 4 2 42 1 5 21 3 1 12

� − � �− − � �− − − ��

2. a. (6, -2, 5) b. (6, 4, 2) c. (-2a + 6, -a – 2, a) 3. (1, -2, 4) 4. no solution 5. 750 $10 tickets, 500 $20 tickets, 250 $50 tickets

6. 3 55 8

� � �−� �

7. a.

9 00 46 7

� � � � ��

b.

2 510 83 21

−� � �− � ��

c. impossible

8.

27 111 11

6 12

� � � � �−� �

9. 1 5 4 5 1 01 4 1 1 0 1

−� � � � � �= � � �−� � � � � �

10. a. 4 33 2� � ��

b. (5, 1)

11. 30 units of Product A, 60 units of Product B, 50 units of Product C 12. (1, 3)


50 Answers for Chapter 5 Test Form B

1.

2 1 6 53 1 2 71 1 4 8

� − � �− � �− − ��

2. a. (8, 3, -2) b. (6, -2, 2) c. no solution 3. (6, 1, -1) 4. no solution 5. $20,000 at 8%, $20,000 at 10%, $40,000 at 14%

6. 10 6

9 5� � �− −� �

7. a.

28 24 16

18 28

� � �− � ��

b.

7 48 46 21

−� � �− � �− −� �

c. impossible

8.

5 62 2412 36

−� � �− � �−� �

9. 4 1 1 1 1 03 1 3 4 0 1

−� � � � � �= � � �−� � � � � �

10. a. 1 2.51 3

−� � �−� �

b. (-1, 3)



Answers for Chapter 5 Test Form C 51

1.

1 4 3 22 4 7 64 2 1 2

� − � �− � �− − − ��

2. a. (5, -1, -6) b. (6, 2, 3) c. no solution 3. (-2, 2, 3) 4. (0.5a + 0.5, 2.5a + 1.5, a) 5. 1200 $10 tickets, 400 $20 tickets, 200 $50 tickets

6. 19 27

9 28−� �

�−� �

7. a.

6 04 96 2

� � � � �−� �

b.

7 522 73 6

− −� � � � �−� �

c. impossible

8.

14 010 63 13

� � �− � �−� �

9. 3 7 2 7 1 01 2 1 3 0 1

−� � � � � �= � � �−� � � � � �

10. a. 1 13 4

−� � �−� �

b. (3, -2)



-4 -2 2 4

-4

-2

2

4

-4 -2 2 4

-4

-2

2

4

2 4 6 8 10

-10

-5

5

10

15

20

25

2 4 6 8 10

-10

-5

5

10

15

20

25

52 Answers for Chapter 6 Test Form A 1. 2. (0, 4), (4, 2), (2, 0) 3. corner points (2, 16) and (5, 25) 4. (0, 5) 5. (3, 6) 30f = 6. a. geometric b. arithmetic 7. -12,288 8. 10.368 feet 9. 7625

10. 37

11. 4 3 1/ 413 4

2y x x x− − −= − +

12. 1 5

,6,2 3

x = −


-4 -2 2 4

-2

2

4

-4 -2 2 4

-2

2

4

2 4 6 8

2.5

5

7.5

10

12.5

15

2 4 6 8

2.5

5

7.5

10

12.5

15

Answers for Chapter 6 Test Form B 53 1. 2. (0, 4), (-2, 0), (4, 0) 3. corner points (2, 16) and (6, 16) 4. (2, 4) 5. (2, 2) 10f = 6. a. arithmetic b. geometric 7. -354,294 8. 12.96 feet 9. 4425

10. 23

11. 5 3 1/312 5

3y x x x− − −= − +

12. 1 1

, 2,4 3

x = − −


-4 -2 2 4

-5

-4

-3

-2

-1

1

-4 -2 2 4

-5

-4

-3

-2

-1

1

0 . 5 1 1 . 5 2 2 . 5 3

- 6

- 4

- 2

2

4

6

8

0 . 5 1 1 . 5 2 2 . 5 3

- 6

- 4

- 2

2

4

6

8

54 Answers for Chapter 6 Test Form C 1. 2. (6, 0), (2, 2 2/3), (18, 0) 3. corner points (0, 8) and (3, -7) 4. (3, 2) 5. (20, 0) 420f = 6. a. geometric b. arithmetic

7. 3

1024−

8. 32.768 feet 9. 9960

10. 73

11. 7 6 2 /332 4

2y x x x− − −= − +

12. 2

1, 4,3

x = −


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