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Solution Manual for Algebra and Trigonometry with Modeling and Visualization, 6th Edition

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    T ESTING M ANUAL M ATH M ADE V ISIBLE A LGEBRA AND T RIGONOMETRY WITH M ODELING AND V ISUALIZATION P RECALCULUS WITH M ODELING AND V ISUALIZATION S IXTH E DITION Gary Rockswold Minnesota State University, Mankato with Terry Krieger Rochester Community an d Technical College and Jessica Rockswold

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    Table of Contents Chapter 1 Introduction to Functions and Graphs 1 Chapter 2 Linear Functions and Equations 17 Chapter 3 Quadratic Functions and Equations 35 Chapter 4 More Nonlinear Functions and Equations 51 Chapter 5 Exponential and Logarithmic Functions 69 Chapter 6 Trigonometric Functions 85 Chapter 7 Trigonometric Identities and Equations 103 Chapter 8 Further Topics in Trigonometry 115 Chapter 9 Systems of Equations and Inequalities 127 Chapter 10 Conic Sections 147 Chapter 11 Further Topics in Algebra 163

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    1 Name _______________________________ Rockswold College Algebra & Trigonometry Chapter 1 Test–Form A 1. Let a function f be represented symbolically by 2 ( ) 8 . f x x   Find ( 1). f  1. _____ (A) 9 (B) 10 (C) 7 (D) 6  2. Determine which set of ordered pairs does not represent a function. 2. _____ (A) {(1, 1), (0, 2), (1, 3), (0, 2)} (B) {(1, 1), (2, 2), (3, 3), (4, 2)} (C) {(1, 4), (2, 3), (3, 1), (4, 1)} (D) {(1, 1), (2, 0), (3, 1), (4, 0)} 3. Use the graph of f to determine its domain. 3. _____ (A)   1,   (B)   1, 2  (C)   2,   (D)   ,   4. Lake Buchanan, one of the Highland lakes located in central Texas, covers 4. _____ 1.12 8 10  square feet and contains a total volume of 9 4.10 10  cubic feet of water. Find the average depth of Lake Buchanan. (A) 3.66 feet (B) 366 feet (C) 1 3.66 10 feet   (D) 36.6 feet 5. If possible, find the slope of the line passing through ( 2.8, 6.3)  and ( 4.3, 1.5).  5. _____ (A) 0.3125 (B) 3.2  (C) undefined (D) 3.2 6. The table displays the monthly rainfall for Hilo, Hawaii, for the first six months 6. _____ in a typical year. Find the mean rainfall to the nearest tenth of an inch for these six months. Month Jan Feb Mar Apr May Jun Rainfall (inches) 26.1 19.0 10.8 7.4 15.0 7.2 (A) 12.9 in. (B) 14.3 in. (C) 18.7 in. (D) 85.5 in.

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    Chapter 1 Test–Form A Rockswold College Algebra & Trigonometry 2 7. Use the graph of f to evaluate ( 2). f  7. _____ (A) 1  (B) 2.5 (C) 3 (D) 4.8  8. Find the domain of 1 ( ) . 4 f x x   8. _____ (A) 4 x  (B)   4,  (C)   , 4  (D)     , 4 4,    9. Find the midpoint of the line segment joining the points (5.3, 6.1)  and ( 2.8, 1.1).  9. _____ (A) (1.25, 2.5)  (B) (4.05, 3.6)  (C) ( 0.4, 0.85)   (D) (5.7, 195)  10. Find the equation of the circle. 10. _____ (A) 2 2 ( 2) ( 1) 4 x y     (B) 2 2 ( 2) ( 1) 16 x y     (C) 2 2 ( 2) ( 1) 4 x y     (D) 2 2 ( 2) ( 1) 16 x y     11. Find the distance between the points (12.1, 13.5) and ( 5.6, 10.1)   to the nearest tenth. 11. _____ (A) 53.8 (B) 29.5 (C) 41.3 (D) 9.9 12. Find the domain and range of the relation 12. _____ {( 5.2, 1.6), (3.5, 2.9), ( 4.9, 3.2), (6.5, 1.0), ( 2.1, 6.1)}. S       (A) D { 5.2, 1.6, 3.5, 2.9, 4.9}     (B) D {1.6, 2.9, 3.2, 1.0, 6.1}    R {3.2, 6.5, 1.0, 2.1, 6.1}    R { 5.2, 3.5, 4.9, 6.5, 2.1}     (C) D { 1.5, 6.0, 1.2, 9.4, 1.7}    (D) D { 5.2, 3.5, 4.9, 6.5, 2.1}     R {4.9, 1.4, 6.2, 1.2, 4.1}    R {1.6, 2.9, 3.2, 1.0, 6.1}    Test Page 2

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    Chapter 1 Test–Form A Rockswold College Algebra & Trigonometry 3 13. In 2000 the population of Juneau, Alaska was 30,711 and in 2010 it was 31,275 13. _____ Use the midpoint formula to estimate Juneau’s population in 2005. (A) 30,183 (B) 30,311 (C) 30,366 (D) 30,993 14. The data displayed in the table are linear. State the slope m of the line passing 14. _____ through the data points. X 1  0 1 2 3 Y 8  5  2  1 4 (A) 3 m   (B) 1 3 m  (C) 3 m  (D) 1 3 m   15. Which of the following is not the graph of a function? 15. _____ 16. Write a symbolic representation (formula) of a function g that computes 16. _____ the number of dollars in x dimes. (A) ( ) 10 x g x  (B) ( ) 10 g x x  (C) ( ) 0.10 x g x  (D) 10 ( ) g x x  17. The function P defined by 17. _____ 2 ( ) 4 33 P t t t    models the number of diagnostic machines produced by a medical equipment manufacturer yearly, where 0 t  corresponds to the first year of production, 2000. Find the average rate of change in the number of machines produced per year between 2005 and 2010. (A) 25 machines/year (B) 17 machines/year (C) 19 machines/year (D) 40 machines/year Test Page 3

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    Chapter 1 Test–Form A Rockswold College Algebra & Trigonometry 4 18. Plot the relation {( 3, 1), (2, 1), (5, 3)}   in the xy -plane. 18. _____ 19. The table shows the Pizzazz - Zee corporation’s monthly income for the first 6 months 19. _____ of last year in thousands of dollars. Find its median monthly income for this period to the nearest thousand dollars. Month Jan Feb Mar Apr May Jun Income 32 312 92 212 272 188 (A) $185,000 (B) $554,000 (C) $200,000 (D) $280,000 20. Use the graph to determine the intervals on which f is increasing and where it is 20. _____ decreasing. (A) Increasing:     , 5 3,    Decreasing:   3,1  (B) Increasing     , 3 1,    Decreasing:   3,1  (C) Increasing:   3,   Decreasing:   5,  (D) Increasing:   1,  Decreasing:   3,   Test Page 4

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    5 Name _______________________________ Rockswold College Algebra & Trigonometry Chapter 1 Test–Form B 1. Let a function f be represented symbolically by 2 ( ) 10 . f x x   Find ( 3). f  1. _____ (A) 34 (B) 16  (C) 19 (D) 1 2. Use the graph of f to determine its domain. 2. _____ (A)   6,5  (B)   3, 6  (C)   ,   (D)   2.7,5.7  3. If possible, find the slope of the line passing through (2.1, 5.3)  and (5.6, 10.9).  3. _____ (A) 1.6  (B) 0.625  (C) undefined (D) 1.6 4. Lake Mead, formed by the construction of the Hoover Dam, covers 8 7.59 10  4. _____ square feet and contains a total volume of 11 1.37 10  cubic feet of water. Find the average depth of Lake Mead. (A) 180.5 feet (B) 1,805 feet (C) 3 1.805 10 feet   (D) 18.05 feet 5. Determine which set of ordered pairs does not represent a function. 5. _____ (A) {(1, 2), (2, 0), (3, 0), (4, 4)}  (B) {(1, 4), (2, 0), (3, 0), (4, 2)}  (C) {(4, 1), (0, 2), (0, 3), (4, 4)} (D) {(1, 1), (2, 0), (3, 0), (4, 4)}  6. The table displays the monthly rainfall for Hilo, Hawaii, for the last six months 6. _____ in a typical year. Find the mean monthly rainfall to the nearest tenth of an inch for these six months. Month Jul Aug Sep Oct Nov Dec Rainfall (inches) 7.0 13.7 8.1 6.5 2.9 10.5 (A) 48.7 in. (B) 7.6 in. (C) 24.4 in. (D) 8.1 in.

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    Chapter 1 Test–Form B Rockswold College Algebra & Trigonometry 6 7. Use the graph of f to evaluate ( 2). f  7. _____ (A) 0 (B) 1 (C) 5 (D) 3.3  8. Find the domain of 1 ( ) . 5 f x x   8. _____ (A) 5 x  (B)   ,5  (C)   5,  (D)     ,5 5,    9. Find the midpoint of the line segment joining the points ( 3.1, 6.5)   and (6.8, 3.7).  9. _____ (A) ( 4.95, 1.4)   (B) ( 4.8, 1.55)  (C) (1.7, 5.25) (D) (1.85, 5.1)  10. Find the equation of the circle. 10. _____ (A) 2 2 ( 1) ( 1) 25 x y     (B) 2 2 ( 1) ( 1) 5 x y     (C) 2 2 ( 1) ( 1) 25 x y     (D) 2 2 ( 1) ( 1) 5 x y     11. Find the distance between the points ( 7.3, 1.47)   and ( 4.5, 1.47)  to the nearest 11. _____ hundredth. (A) 5.74 (B) 16.48 (C) 11.80 (D) 4.06 12. Find the domain and range of the relation 12. _____ {(1.7, 3.2), ( 3.7, 2.3), ( 2.5, 3.7), (5.3, 4.1), (2.9, 1.2)}. S       (A) D { 3.2, 2.3, 3.7, 4.1, 1.2}     (B) D {1.7, 3.7, 2.5, 5.3, 2.9}    R {1.7, 3.7, 2.5, 5.3, 2.9}    R { 3.2, 2.3, 3.7, 4.1, 1.2}     (C) D {1.7, 3.2, 3.7, 2.3, 2.5}      (D) D { 1.5, 6.0, 1.2, 9.4, 1.7}    R {3.7, 5.3, 4.1, 2.9, 1.2}   R {4.9, 1.4, 6.2, 1.2, 4.1}    Test Page 2

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    Chapter 1 Test–Form B Rockswold College Algebra & Trigonometry 7 13. In 2000 the population of Albuquerque, New Mexico was 448,362 and in 13. _____ 2010 it was 545,852. Use the midpoint formula to estimate Albuquerque’s population in 2005. (A) 497,107 (B) 498,298 (C) 500,135 (D) 496,641 14. The data displayed in the table are linear. State the slope m of the line passing 14. _____ through the data points. X 2  0 2 4 6 Y 4 1 2  5  8  (A) 3 2 m   (B) 2 3 m  (C) 2 3 m   (D) 3 2 m  15. Which of the following is not the graph of a function? 15. _____ 16. Write a symbolic representation (formula) of a function g that computes the 16. _____ number of dimes in x dollars. (A) ( ) 0.10 g x x  (B) ( ) 10 x g x  (C) ( ) 10 g x x  (D) ( ) 0.10 x g x  17. The function P defined by 17. _____ 2 ( ) 2.5 0.5 12 P t t t    models the number of diagnostic machines produced by a medical equipment manufacturer yearly, where 0 t  corresponds to the first year of production, 2000. Find the average rate of change in the number of machines produced yearly between 2005 and 2010. (A) 28 machines/year (B) 190 machines/year (C) 38 machines/year (D) 95 machines/year Test Page 3

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    Chapter 1 Test–Form B Rockswold College Algebra & Trigonometry 8 18. Plot the relation {( 3, 1), ( 3, 2), (5, 4)}    in the xy -plane. 18. _____ 19. Use the graph to determine the intervals on which f is increasing and which it is 19. _____ decreasing. (A) Increasing:   7, 1  Decreasing: ( , 7) (1, )    (B) Increasing: ( 7, )   Decreasing: (1, )  (C) Increasing:   0, 4 Decreasing: [ , 0) (4, )   (D) Increasing: (0, )  Decreasing: (4, )  20. The table shows the Pizzazz-Zee corporation’s income for the first 6 months 20. _____ of last year in thousands of dollars. Find its median monthly income for this period to the nearest thousand dollars. Month Jan Feb Mar Apr May Jun Income 193 171 257 329 379 221 (A) $239,000 (B) $258,000 (C) $208,000 (D) $920,000 Test Page 4

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    9 Name _______________________________ Rockswold College Algebra & Trigonometry Chapter 1 Test–Form C 1. Let a function f be represented symbolically by 2 ( ) 11 . f x x   Find ( 5). f  1. ____________ 2. Lake Roosevelt, formed by the construction of the Grand Coulee Dam, 2. ____________ covers 8 3.98 10  square feet and contains a total volume of 10 2.51 10  cubic feet of water. Find the average depth of Lake Roosevelt to the nearest tenth of a foot. 3. Use the graph of f to determine its domain. 3. ____________ 4. If possible, find the slope of the line passing through ( 1.7, 5.3)   and 4. ____________ (0.1, –9.8). 5. Determine which set of ordered pairs does not represent a function. 5. ____________ (A) {(1, 2), (2, 4), (3, 0), (4, 2)} (B) {(1, 8), (2, 2), (3, 0), (4, 4)}  (C) {( 1, 1), ( 2, 2), ( 1, 3), (0, 4)}    (D) {(1, 4), (2, 4), (3, 4), (4, 4)} 6. The table displays the monthly rainfall for Tampa, Florida, for the 6. ____________ first six months in a typical year. Find the mean monthly rainfall to the nearest hundredth of an inch for these six months. Month Jan Feb Mar Apr May Jun Rainfall (inches) 2.2 2.7 2.8 1.8 2.9 5.5 7. Use the graph of f to evaluate (0). f 7. ____________

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    Chapter 1 Test–Form C Rockswold College Algebra & Trigonometry 10 8. Find the domain of ( ) 10. f x x   8. ____________ 9. Find the midpoint of the line segment joining the points (4.1, 1.9) and 9. ____________ (6.1, 3.5). 10. Find the equation of the circle. 10. ____________ 11. Find the distance between the points (11.2, 8.9)  and (2.7, 11.5) to the 11. ____________ nearest tenth. 12. Find the domain and range of the relation 12. ____________ {( 4.8, 1.2), (1.5, 2.7), (3.2, 5.4), (1.9, 5.1), (2.9, 1.7)}. S      13. In 2000 the population of Austin, Texas was 659,627 and in 2010 it was 13. ____________ 790,390. Use the midpoint formula to estimate Austin’s population in 2005. 14. The data displayed in the table are linear. State the slope m of the line 14. ____________ passing through the data points. X 4  2  0 2 4 Y 13  8  3  2 7 15. Which of the following is not the graph of a function? 15. ____________ Test Page 2

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    Chapter 1 Test–Form C Rockswold College Algebra & Trigonometry 11 16. Write a symbolic representation (formula) of a function f that computes the 16. ____________ number of ounces in x pounds. 17. The function P defined by 17. ____________ 2 ( ) 1.5 2.5 42 P t t t    models the number of diagnostic machines produced by a medical equipment manufacturer yearly, where 0 t  corresponds to the first year of production, 2000. Find the average rate of change in the number of machines produced yearly between 2005 and 2010. 18. Plot the relation {( 3, 7), ( 1, 3), ( 5, 3), (8, 1), (2, 2)} S       in the xy -plane . 18. ____________ 19. Use the graph to determine the intervals on which f is increasing and 19. ____________ on which it is decreasing. 20. The table shows the Pizzazz-Zee corporation’s income for the first 6 months 20. ____________ of last year in thousands of dollars. Find its median monthly income for this period to the nearest thousand dollars. Month Jan Feb Mar Apr May Jun Income 127 93 173 125 137 149 Test Page 3

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    12 Name _______________________________ Rockswold College Algebra & Trigonometry Chapter 1 Test–Form D 1. Let a function f be represented symbolically by 2 ( ) 12 . f x x   Find ( 6). f  1. ____________ 2. Lake Powell, formed by the construction of the Glen Canyon Dam, covers 2. ____________ 7.78 8 10  square feet and contains a total volume of 10 9.84 10  cubic feet of water. Find the average depth of Lake Powell to the nearest tenth of a foot. 3. Use the graph of f to determine its domain. 3. ____________ 4. If possible, find the slope of the line passing through (4.2, 1.3)  and (7.4, 3.5). 4. ____________ 5. Determine which set of ordered pairs does not represent a function. 5. ____________ (A) {(1, 2), (2, 4), (3, 6), (4, 8)} (B) {(8, 4), (6, 3), (4, 2), (2, 1)} (C) {( 1, ), ( 2, ), ( 3, ), ( 4, )}         (D) {( , 1), ( , 2), ( , 3), ( , 4)}     6. The table displays the monthly rainfall for Tampa, Florida, for the last six months 6. ____________ in a typical year. Find the mean monthly rainfall to the nearest hundredth of an inch for these six months. Month Jul Aug Sep Oct Nov Dec Rainfall (inches) 6.4 7.6 6.5 2.4 1.6 2.3 7. Use the graph of f to evaluate (2). f 7. ____________ 8. Find the domain of ( ) 8 . f x x   8. ____________ 9. Find the midpoint of the line segment joining the points ( 1.3, 5.7)  9. ____________ and (4.6, 2.1).

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    Chapter 1 Test–Form D Rockswold College Algebra & Trigonometry 13 10. Find the equation of the circle. 10. ____________ 11. Find the distance between the points (1.81. 8.13) and ( 5.11, 2.94)  to the 11. ____________ nearest hundredth. 12. Find the domain and range of the relation 12. ____________ {(4.8, 2.1), (5.2, 1.9), ( 1.7, 4.3), (2.2, 3.9), ( 4.9, 1.1)}. S       13. In 2000 the population of Portland, Oregon was 529,209 and in 2010 it 13. ____________ was 583,776. Use the midpoint formula to estimate Portland’s population in 2005. 14. The data displayed in the table are linear. State the slope m of the line 14. ____________ passing through the data points. X 9  5  1  3 7 Y 3 2 1 0 1  15. Which of the following is not the graph of a function? 15. ____________ 16. Write a symbolic representation (formula) of a function f that computes the 16. ____________ number of pounds in x ounces. Test Page 2

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