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Solution Manual for College Algebra with Intermediate Algebra A Blended Course

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    O NLINE T EST B ANK C OLLEGE A LGEBRA WITH I NTERMEDIATE A LGEBRA A B LENDED C OURSE Judith A. Beecher Judith A. Penna Barbara L. Johnson Ivy Tech Community College of Indiana Marvin L. Bittinger Indiana University Purdue University Indianapolis

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    iii CONTENTS I. ALTERNATE TESTS, FORMS A, B, C, D, E, and F .......................................................... 1 There are six alternate test forms for each chapter and the final examination. Alternate Test Forms A, B, C, and D are equivalent in length and difficulty. Synthesis questions occur at the end of the Test Forms, and are separated from the rest of the test by a solid line. Synthesis questions are meant to be more challenging than the previous test questions, like those problems found in the last part of each exercise set in the text. The synthesis questions have been placed at the end to make it easy to omit them if the instructor wishes to do so. Questions on Test Forms E and F are multiple choice. Effort was made to make the wrong answers as logically wrong as possible. In most cases answers were constructed to avoid students doing backward reasoning. This Instructor’s Online Test Bank is designed to accompany College Algebra with Intermediate Algebra: A Blended Course by Beecher/Penna/Johnson/Bittinger. Chapter R ........................................................................................................................... R-1 Chapter 1 ................................................................................................................................ 1 Chapter 2 .............................................................................................................................. 25 Chapter 3 .............................................................................................................................. 49 Chapter 4 .............................................................................................................................. 73 Chapter 5 .............................................................................................................................. 97 Chapter 6 ............................................................................................................................ 121 Chapter 7 ............................................................................................................................ 145 Chapter 8 ............................................................................................................................ 169 Chapter 9 ............................................................................................................................ 193 Chapter 10 .......................................................................................................................... 221 Chapter 11 .......................................................................................................................... 237 Chapter 12 .......................................................................................................................... 261 II. FINAL EXAMINATIONS................................................................................................. 289 III. ANSWER KEYS FOR ALTERNATE TESTS, FORMS A, B, C, D, E, and F ................ 345 IV. ANSWER KEYS FOR FINAL EXAMINATIONS........................................................... 390 Thanks are extended to Mike Penna for producing the graphs and to Kelly Barber for typing the manuscript.

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    289 Year Number candles sold 0 80 1 70 2 62 3 64 FINAL EXAMINATION NAME_____________________________ TEST FORM A CLASS_____SCORE_____GRADE_____ ___________________________________________________________________________ 1. Simplify:   3 4 5 2 a b    . 2. Graph 2 x  on a number line. 3. Divide: 6 8 2.4 10 3.2 10    . Write scientific notation for the answer. 4. Find the union:     2,3,8,11,16 3,5,8,12  . 5. Determine whether the correspondence is a function. 2 Mary 3 Jeff 4 Anthony Deirdre 6. Find an equation of the line parallel to 4 2 3 x y   which passes through   2, 5  . 7. The table below shows the number of candles sold at a charity’s fundraiser for 4 successive years. Use years 0 and 3 to model the data with a linear function, and then predict the number of candles that will be sold in year 5 using this function. ANSWERS 1. 2. See graph. 3. 4. 5. 6. 7.

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    290 FINAL EXAMINATION NAME_____________________________ TEST FORM A ___________________________________________________________________________ ANSWERS 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. a) b) 23. a) b) 24. a) b) 25. a) b) Solve. 8. 6 2 4 = − x 9. 0 3 5 2 = + − x x 10. 1 2 2 + = + x x 11. 15 8 2 − > x x 12. x x x 4 4 2 27 3 3 − = 13. log 8 x  14. 4 3 8 7 5 4 x x    15. 2 2 1 1 2 1 2 x x x x x     . Solve, if possible. If there is no solution, state this. Use any method. 16. 2 6 2, 7 x y x y + = − = − 17. 3 2 6, 2 5 3 26, 3 2 8 x y z x y z x y z − + = − + + = − − + − = 18. 2 6, 2 4 12 x y x y + = + = − 19. 2 2 2 5 38, 6 16 x y x y      20. Solve and write interval notation for the solution set: 3 4 2 14 x     . 21. Given that     2 2 1 3, f x x    find: a)   4 ; f b)   2 . f a  For     and 3 1, f x x g x x    find each of the following: 22. a) The domain of f ; b) the domain of g . 23. a)     ; f g x  b) the domain of f g  . 24. a)     / ; g f x b) the domain of / g f . 25. a)     ; g f x  b) the domain of g f  .

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    291 FINAL EXAMINATION NAME_____________________________ TEST FORM A ___________________________________________________________________________ 26. The graph of the function   y f x  is shown below on the left. No formula for f is given. Make graph of   3 y f x   . Graph the equation. 27. 4 y x    28. 1 2 y x     29. Graph: ( ) 1 − = x e x f . ANSWERS 26. See graph. 27. See graph. 28. See graph. 29. See graph.

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    292 FINAL EXAMINATION NAME_____________________________ TEST FORM A ___________________________________________________________________________ ANSWERS 30. See graph. 31. See graph. 32. See graph. 33. a) b) c) d) e) f) See graph. 30. Make a graph of 2 2. x y + < − 31. Graph     2 4 2 f x x   . Label all the asymptotes and any intercepts. 32. Graph     2 2 1 2 1 4 9 x y     . 33. For the graph of the function ( ) 2 2 4 5, f x x x = + + a) find the vertex; b) find the axis of symmetry; c) state whether there is a maximum or minimum value and find that value; d) find the range; e) determine the intervals on which the function is increasing, decreasing, and constant; f) graph the function.

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    293 FINAL EXAMINATION NAME_____________________________ TEST FORM A ___________________________________________________________________________ 34. Graph: 3 x   . 35. Find the asymptotes of the hyperbola given by 2 2 4 5 100 x y   . 36. Find the center and the radius of a circle given by 2 2 8 10 23 0. x x y y + + − − = 37. Determine whether the graph of 5 y x = is symmetric with respect to the x -axis, the y -axis, and/or the origin. 38. Find the maximum value and minimum value of 15 F x y = + subject to 5, 3 2 6, 0, 10. x y x y x y + ≥ − ≤ ≥ ≤ 39. For   4 3 2 3 5 6 4 2, f x x x x x      what does Descartes’ rule of signs tell you about: a) the number of positive real zeros, b) the number of negative real zeros? 40. Suppose that a polynomial function of degree 5 with rational coefficients has i − − 3 and , 5 2, as zeros. Find the other zeros. . ANSWERS 34. See graph. 35. 36. 37. 38. 39. a) b) 40.

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    294 FINAL EXAMINATION NAME_____________________________ TEST FORM A ___________________________________________________________________________ ANSWERS 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. Use A =       − 7 0 1 2 1 3 , B =       − 5 4 3 2 for Exercises 41 and 42. 41. Find BA , if possible. 42. Find B 1 − , if possible. 43. Evaluate the determinant. 2 1 0 3 2 1 5 4 3 − − − Perform the indicated operations and simplify. 44. 2 2 6 4 3 xy xy xy xy    45.     3 3 2 5 3 2 6 2 3 x x x x x       46.   2 3 8 x  47. 3 1 8  48. 2 2 2 3 10 4 x x x x     49. 2 2 3 2 9 5 6 27 3 9 x x x x x x        50. Multiply:     3 2 5 i i   . 51. Divide:     4 3 2 3 2 2 x x x x      . 52. Use the laws of exponents to simplify. Write answers with positive exponents.   1/ 2 3/8 2/5 a b   . Factor. 53. 2 15 14 16 n n   54. 2 2 2 4 4 4 a ab b c    55. Find the formula for the inverse of   5 , x f x x   if possible.

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    295 FINAL EXAMINATION NAME_____________________________ TEST FORM A ___________________________________________________________________________ 56. Find an equation of variation in which y varies directly as x , and 0.8 y = when 6. x = 57. Given that 5000 . 0 2 log and 7925 . 1 12 log = = b b , find 6 log b . 58. The population of a bacteria culture doubled in 6 hr. What was the exponential growth rate? 59. You are taking a history course in which there will be 4 tests, each worth 100 points. You have scores of 84, 71, and 79. You must have a total of at least 320 points in order to get a B. What scores on the last test will give you at least a B? 60. An airplane flew 4 hr with a 25-mph tailwind and returned in 4.5 hr against the same wind. How fast can the plane fly in still air? 61. In a right triangle with legs 5 and 7 a b   , find hypotenuse c . Give an exact answer and an approximation to three decimal places. 62. Amount of an Annuity . To create a college fund, a parent makes a sequence of 15 yearly deposits of $3000 each in a savings account on which interest is compounded annually at 4.5%. Find the amount of the annuity. 63. How many license plates can be formed using three letters followed by 3 digits? 64. Card Drawing . Suppose we draw a card from a well-shuffled deck of 52 cards. What is the probability of drawing a king or a two? 65. The 1st term of an arithmetic sequence is 3 − and the 13th term is 6. Find the 8th term. 66. Evaluate:     5 1 1 3 2 k k k     . 67. If 1 1 4 2, and 2 1, find . n n a a a a + = − = − ANSWERS 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67.

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    296 FINAL EXAMINATION NAME_____________________________ TEST FORM A ___________________________________________________________________________ ANSWERS 68. 69. 70. 71. 72. 68. Use mathematical induction to prove that for every natural number n ,   4 8 12 4 1 . n n n          69. Find: 10 3 . C 70. The graph of the function   g x is shown at the right. The graph of     2 1 f x g x   is which of the following? A. B. C. D. _______________________________________________________ 71. Find the domain of 2 − x x . 72. If ( ) 6 , 4 − is on the graph of ( ) x f y = , what point do you know is on the graph of ( ) 2 − x f ?

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    297 FINAL EXAMINATION NAME_____________________________ TEST FORM B CLASS_____SCORE_____GRADE_____ ___________________________________________________________________________ 1. Evaluate 4 3 x y x  when 3 and 8 x y    . 2. Simplify:   5 5 7 x y   . 3. Convert to scientific notation: 0.0543. 4. Write interval notation for   8 5 x x    . 5. Find the distance between 3.4  and 7.6. 6. Is the graph at right a graph of a function? 7. Determine whether the pair of lines are parallel, perpendicular, or neither. 2 3 6, 3 2 8. x y x y      8. The table below shows the number of trips over 50 mi made for 4 successive years. Use years 1 and 3 to model the data with a linear function, and then predict the number of trips over 50 mi in year 6 using this function. ANSWERS 1. 2. 3. 4. 5. 6. 7. 8. Year, x Number of trips over 50 mi, T 0 20 1 22 2 30 3 32

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    298 FINAL EXAMINATION NAME_____________________________ TEST FORM B ___________________________________________________________________________ ANSWERS 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. a) b) Solve. 9. 2 11 1 2 3 5 = − + − + x x x 10. 0 8 2 = − − n n 11. 2 4 6 0 x x    12. 6 4 7 5 x   13. x x 3 6 16 2 = − 14. 1 . 0 ln = x 15. 7 3 7 x    16. 4 3 1 2 5 9 x and x     17. 2 7 9 x x   . Give exact solutions and approximate solutions to three decimal places. Solve, if possible. If there is no solution, state this. Use any method. 18. 12 7 5 = − y x , 19. 8 2 3 − = + − z y x , 6 14 10 − = + − y x 10 8 3 4 − = + − − z y x , 13 4 2 = + + z y x 20. Solve: 31 2 = + y x , 16 − = xy . 21. a) Solve by graphing: 4 2, 3. y x x y     b) Classify the system as consistent or inconsistent and the equations as dependent or independent.

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    299 FINAL EXAMINATION NAME_____________________________ TEST FORM B ___________________________________________________________________________ For ( ) 3 − = x x f and ( ) 1 2 + = x x g , find each of the following: 22. a) The domain of f ; b) the domain of g . 23. a) ( )( ) x g f − ; b) the domain of g f − . 24. a) ( )( ) x f g / ; b) the domain of f g / . 25. a) ( )( ) x f g  ; b) the domain of f g  . 26. Write an equation for a function that has the shape of x y = , but shifted left 2 units and up 4 units. Graph the equation. 27. 4 2 1 − = x y 28. 1 2 − − = x y 29. Graph: ( ) 2 + = x e x f . ANSWERS 22. a) b) 23. a) b) 24. a) b) 25. a) b) 26. 27. See graph. 28. See graph. 29. See graph.

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    300 FINAL EXAMINATION NAME_____________________________ TEST FORM B ___________________________________________________________________________ ANSWERS 30. See graph. 31. See graph. 32. See graph. 33. See graph. 34. 30. Graph the system of equations and find the coordinates of any points of intersection. 5 3 , 4 2 3 − ≥ ≥ − x y y x 31. Graph: 3 y x  . 32. Graph: ( ) ( ) 1 9 2 4 1 2 2 = − − + y x . 33. Graph : x x y 2 3 + − = . 34. Determine if the graph of the equation in Exercise 33 is symmetric with respect to the x -axis, the y -axis, and the origin.

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    301 FINAL EXAMINATION NAME_____________________________ TEST FORM B ___________________________________________________________________________ 35. For the graph of the function ( ) x x x f 4 2 + − = , a) find the vertex; b) find the axis of symmetry; c) state whether there is a maximum or minimum value and find that value; d) find the range; e) determine the intervals on which the function is increasing, decreasing, and constant; f) graph the function. 36. Find the center and the radius of the circle given by 0 29 12 8 2 2 = − + + − y y x x . 37. Find a rational function that has vertical asymptotes of 3 = x and 6 − = x , and y -intercept ( ) 2 , 0 . 38. Maximizing Profit . Bruce’s Bakery prepares cakes and muffins. In a given week, 200 products can be prepared of which 50 cakes and 70 dozen muffins are required by regular customers. Each dozen muffins represents one product as muffins are only sold in packages of one dozen. The profit on a cake is $ 2 and on a package of muffins is $ 50 . 1 . How many of each should the bakery make to maximize profit? What is the maximum profit? 39. For ( ) 4 6 3 2 2 3 5 − + − = x x x x f , what does Descartes’ rule of signs tell you about: a) the number of positive real zeros; b) the number of negative real zeros? 40. Use the intermediate value theorem to determine whether ( ) 2 4 3 + − = x x x f has a real zero between 0 and 1 − , if possible. Show your work. If it is not possible to make a determination using this method, state this. Use A =       − − 8 2 4 2 5 1 , B =       − − 5 4 3 2 for Exercises 41 and 42. 41. Find AB , if possible. 42. Find B 1 − , if possible. ANSWERS 35. a) b) c) d) e) f) See graph. 36. 37. 38. 39. a) b) 40. 41. 42.

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