Skip to content
Textbook Guides

Solution Manual for Precalculus Enhanced with Graphing Utilities, MyLab Math, 8th Edition

Find textbook answers quickly with Solution Manual for Precalculus Enhanced with Graphing Utilities, MyLab Math, 8th Edition, a detailed solutions manual designed to make studying easier.

Preview 16 of 1592 pages

See the first 16 pages exactly as they appear in the document.

  1. Page 1
    Read page 1 as text

    S OLUTIONS M ANUAL T IM B RITT Jackson State Community College P RECALCULUS E NHANCED WITH G RAPHING U TILITIES E IGHTH E DITION Michael Sullivan Chicago State University Michael Sullivan III Joliet Junior College

  2. Page 2
  3. Page 3
    Read page 3 as text

    Table of Contents Chapter 1 Graphs 1.1 Graphing Utilities; Introduction to Graphing Equations ......................................................... 1 1.2 The Distance and Midpoint Formulas ..................................................................................... 8 1.3 Intercepts; Symmetry; Graphing Key Equations ................................................................... 20 1.4 Solving Equations Using a Graphing Utility ......................................................................... 36 1.5 Lines ...................................................................................................................................... 41 1.6 Circles .................................................................................................................................... 58 Chapter Review .............................................................................................................................. 72 Chapter Test ................................................................................................................................... 79 Chapter Projects ............................................................................................................................. 82 Chapter 2 Functions and Their Graphs 2.1 Functions ............................................................................................................................... 83 2.2 The Graph of a Function ...................................................................................................... 101 2.3 Properties of Functions ........................................................................................................ 110 2.4 Library of Functions; Piecewise-defined Functions ............................................................ 127 2.5 Graphing Techniques: Transformations .............................................................................. 139 2.6 Mathematical Models: Building Functions.......................................................................... 157 Chapter Review ............................................................................................................................ 165 Chapter Test ................................................................................................................................. 172 Cumulative Review ...................................................................................................................... 175 Chapter Projects ........................................................................................................................... 179 Chapter 3 Linear and Quadratic Functions 3.1 Properties of Linear Functions and Linear Models.............................................................. 181 3.2 Building Linear Functions from Data .................................................................................. 192 3.3 Quadratic Functions and Their Properties ........................................................................... 198 3.4 Build Quadratic Models from Verbal Descriptions and from Data ..................................... 222 3.5 Inequalities Involving Quadratic Functions ......................................................................... 230 Chapter Review ............................................................................................................................ 249 Chapter Test ................................................................................................................................. 257 Cumulative Review ...................................................................................................................... 260 Chapter Projects ........................................................................................................................... 263 Chapter 4 Polynomial and Rational Functions 4.1 Polynomial Functions .......................................................................................................... 266 4.2 The Graph of a Polynomial Function: Models .................................................................... 277 4.3 The Real Zeros of a Polynomial Function ........................................................................... 297 4.4 Complex Zeros; Fundamental Theorem of Algebra ............................................................ 334 4.5 Properties of Rational Functions ......................................................................................... 343 4.6 The Graph of a Rational Function ....................................................................................... 353 4.7 Polynomial and Rational Inequalities .................................................................................. 409 Chapter Review ............................................................................................................................ 431 Chapter Test ................................................................................................................................. 445 Cumulative Review ...................................................................................................................... 449 Chapter Projects ........................................................................................................................... 454

  4. Page 4
    Read page 4 as text

    Chapter 5 Exponential and Logarithmic Functions 5.1 Composite Functions ........................................................................................................... 455 5.2 One-to-One Functions; Inverse Functions ........................................................................... 473 5.3 Exponential Functions ......................................................................................................... 496 5.4 Logarithmic Functions ......................................................................................................... 517 5.5 Properties of Logarithms ..................................................................................................... 539 5.6 Logarithmic and Exponential Equations.............................................................................. 548 5.7 Financial Models ................................................................................................................. 569 5.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models ............................................................................................................... 577 5.9 Building Exponential, Logarithmic, and Logistic Models from Data ................................. 588 Chapter Review ............................................................................................................................ 593 Chapter Test ................................................................................................................................. 605 Cumulative Review ...................................................................................................................... 609 Chapter Projects ........................................................................................................................... 612 Chapter 6 Trigonometric Functions 6.1 Angles, Arc length, and Circular Motion ............................................................................ 615 6.2 Trigonometric Functions; Unit Circle Approach ................................................................. 624 6.3 Properties of the Trigonometric Functions .......................................................................... 642 6.4 Graphs of the Sine and Cosine Functions ............................................................................ 656 6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions................................... 678 6.6 Phase Shift; Sinusoidal Curve Fitting .................................................................................. 688 Chapter Review ............................................................................................................................ 701 Chapter Test ................................................................................................................................. 709 Cumulative Review ...................................................................................................................... 712 Chapter Projects ........................................................................................................................... 716 Chapter 7 Analytic Trigonometry 7.1 The Inverse Sine, Cosine, and Tangent Functions ............................................................... 720 7.2 The Inverse Trigonometric Functions (Continued) ............................................................. 734 7.3 Trigonometric Equations .................................................................................................... 746 7.4 Trigonometric Identities ...................................................................................................... 767 7.5 Sum and Difference Formulas ............................................................................................. 780 7.6 Double-angle and Half-angle Formulas ............................................................................... 805 7.7 Product-to-Sum and Sum-to-Product Formulas................................................................... 833 Chapter Review ............................................................................................................................ 846 Chapter Test ................................................................................................................................. 861 Cumulative Review ...................................................................................................................... 866 Chapter Projects ........................................................................................................................... 872

  5. Page 5
    Read page 5 as text

    Chapter 8 Applications of Trigonometric Functions 8.1 Right Triangle Trigonometry; Applications ........................................................................ 876 8.2 The Law of Sines ................................................................................................................. 890 8.3 The Law of Cosines ............................................................................................................. 905 8.4 Area of a Triangle ................................................................................................................ 917 8.5 Simple Harmonic Motion; Damped Motion; Combining Waves ........................................ 927 Chapter Review ............................................................................................................................ 937 Chapter Test ................................................................................................................................. 943 Cumulative Review ...................................................................................................................... 947 Chapter Projects ........................................................................................................................... 953 Chapter 9 Polar Coordinates; Vectors 9.1 Polar Coordinates ................................................................................................................ 957 9.2 Polar Equations and Graphs................................................................................................. 966 9.3 The Complex Plane; De Moivre’s Theorem ........................................................................ 996 9.4 Vectors ............................................................................................................................... 1008 9.5 The Dot Product................................................................................................................. 1021 9.6 Vectors in Space ................................................................................................................ 1027 9.7 The Cross Product ............................................................................................................. 1034 Chapter Review .......................................................................................................................... 1045 Chapter Test ............................................................................................................................... 1054 Cumulative Review .................................................................................................................... 1058 Chapter Projects ......................................................................................................................... 1060 Chapter 10 Analytic Geometry 10.2 The Parabola ...................................................................................................................... 1064 10.3 The Ellipse ......................................................................................................................... 1080 10.4 The Hyperbola ................................................................................................................... 1097 10.5 Rotation of Axes; General Form of a Conic ...................................................................... 1117 10.6 Polar Equations of Conics ................................................................................................. 1130 10.7 Plane Curves and Parametric Equations ............................................................................ 1139 Chapter Review .......................................................................................................................... 1154 Chapter Test ............................................................................................................................... 1163 Cumulative Review .................................................................................................................... 1168 Chapter Projects ......................................................................................................................... 1170 Chapter 11 Systems of Equations and Inequalities 11.1 Systems of Linear Equations: Substitution and Elimination ............................................. 1174 11.2 Systems of Linear Equations: Matrices ............................................................................. 1197 11.3 Systems of Linear Equations: Determinants ...................................................................... 1222 11.4 Matrix Algebra .................................................................................................................. 1236 11.5 Partial Fraction Decomposition ......................................................................................... 1255 11.6 Systems of Nonlinear Equations ........................................................................................ 1274 11.7 Systems of Inequalities ...................................................................................................... 1302 11.8 Linear Programming .......................................................................................................... 1317 Chapter Review .......................................................................................................................... 1331 Chapter Test ............................................................................................................................... 1346 Cumulative Review .................................................................................................................... 1354 Chapter Projects ......................................................................................................................... 1358

  6. Page 6
    Read page 6 as text

    Chapter 12 Sequences; Induction; the Binomial Theorem 12.1 Sequences .......................................................................................................................... 1360 12.2 Arithmetic Sequences ........................................................................................................ 1374 12.3 Geometric Sequences; Geometric Series ........................................................................... 1383 12.4 Mathematical Induction ..................................................................................................... 1394 12.5 The Binomial Theorem ...................................................................................................... 1404 Chapter Review .......................................................................................................................... 1411 Chapter Test ............................................................................................................................... 1415 Cumulative Review .................................................................................................................... 1418 Chapter Projects ......................................................................................................................... 1421 Chapter 13 Counting and Probability 13.1 Counting ............................................................................................................................ 1424 13.2 Permutations and Combinations ........................................................................................ 1427 13.3 Probability ......................................................................................................................... 1432 Chapter Review .......................................................................................................................... 1439 Chapter Test ............................................................................................................................... 1441 Cumulative Review .................................................................................................................... 1442 Chapter Projects ......................................................................................................................... 1445 Chapter 14 A Preview of Calculus: The Limit, Derivative, and Integral of a Function 14.1 Finding Limits Using Tables and Graphs .......................................................................... 1448 14.2 Algebra Techniques for Finding Limits............................................................................. 1454 14.3 One-sided Limits; Continuity ............................................................................................ 1458 14.4 The Tangent Problem; The Derivative .............................................................................. 1466 14.5 The Area Problem; The Integral ........................................................................................ 1476 Chapter Review .......................................................................................................................... 1490 Chapter Test ............................................................................................................................... 1497 Chapter Projects ......................................................................................................................... 1500 Appendix A: Review A.1 Algebra Essentials ............................................................................................................. 1506 A.2 Geometry Essentials .......................................................................................................... 1511 A.3 Polynomials ....................................................................................................................... 1517 A.4 Synthetic Division ............................................................................................................. 1525 A.5 Rational Expressions ......................................................................................................... 1527 A.6 Solving Equations .............................................................................................................. 1532 A.7 Complex Numbers; Quadratic Equations in the Complex Number System ...................... 1547 A.8 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications ... 1553 A.9 Interval Notation; Solving Inequalities .............................................................................. 1561 A.10 n th Roots; Rational Exponents .......................................................................................... 1572 Appendix B: The Limit of a Sequence; Infinite Series .................................................... 1583

  7. Page 7
    Read page 7 as text

    1 Chapter 1 Graphs Section 1.1 1. 0 2. 3. x- coordinate; y -coordinate; quadrants 4. False; points that lie in Quadrant IV will have a positive x -coordinate and a negative y -coordinate. The point   1, 4  lies in Quadrant II. 5. d 6. c 7. (a) Quadrant II (b) x -axis (c) Quadrant III (d) Quadrant I (e) y -axis (f) Quadrant IV 8. (a) Quadrant I (b) Quadrant III (c) Quadrant II (d) Quadrant I (e) y -axis (f) x -axis 9. The points will be on a vertical line that is two units to the right of the y- axis. 10. The points will be on a horizontal line that is three units above the x-axis. 11.   1, 4  ; Quadrant II 12. (3, 4); Quadrant I 13. (3, 1); Quadrant I

  8. Page 8
    Read page 8 as text

    Chapter 1: Graphs 2 14.   6, 4   ; Quadrant III 15. min 11 max 5 scl 1 min 3 max 6 scl 1 X X X Y Y Y         16. min 3 max 7 scl 1 min 4 max 9 scl 1 X X X Y Y Y         17. min 30 max 50 scl 10 min 90 max 50 scl 10 X X X Y Y Y         18. min 90 max 30 scl 10 min 50 max 70 scl 10 X X X Y Y Y         19. min 10 max 110 scl 10 min 10 max 160 scl 10 X X X Y Y Y         20. min 20 max 110 scl 10 min 10 max 60 scl 10 X X X Y Y Y         21. min 6 max 6 scl 2 min 4 max 4 scl 2 X X X Y Y Y         22. min 3 max 3 scl 1 min 2 max 2 scl 1 X X X Y Y Y         23. min 6 max 6 scl 2 min 1 max 3 scl 1 X X X Y Y Y         24. min 9 max 9 scl 3 min 12 max 4 scl 4 X X X Y Y Y         25. min 3 max 9 scl 1 min 2 max 10 scl 2 X X X Y Y Y       26. min 22 max 10 scl 2 min 4 max 8 scl 1 X X X Y Y Y        

  9. Page 9
    Read page 9 as text

    Section 1.1: Graphing Utilities; Introduction to Graphing Equations 3 27. 4 y x x   4 0 0 0 0 0    4 1 1 1 1 0    4 0 ( 1) 1 0 1 1        (0, 0) is on the graph of the equation. 28. 3 2 y x x   3 0 0 2 0 0 0    3 1 1 2 1 1 1     3 1 1 2 1 1 1       (0, 0) and (1, –1) are on the graph of the equation. 29. 2 2 9 y x   2 2 3 0 9 9 9    2 2 0 3 9 0 18    2 2 0 ( 3) 9 0 18     (0, 3) is on the graph of the equation. 30. 3 1 y x   3 2 1 1 8 2    3 1 0 1 1 1    3 0 1 1 0 0     (0, 1) and (–1, 0) are on the graph of the equation. 31. 2 2 4 x y   2 2 0 2 4 4 4    2 2 ( 2) 2 4 8 4     2 2 2 2 4 4 4      (0, 2) and 2, 2 are on the graph of the equation. 32. 2 2 4 4 x y   2 2 0 4 1 4 4 4     2 2 2 4 0 4 4 4       2 2 1 2 2 4 4 5 4    (0, 1) and (2, 0) are on the graph of the equation. 33. (–1, 0), (1, 0) 34. (0, 1) 35. , 0 , , 0 , (0, 1) 2 2                36. (–2, 0), (2, 0), (0, –3) 37.   1, 0 ,   0, 2 ,   0, 2  38. (2, 0), (0, 2), (–2, 0), (0, –2) 39. (–4,0), (–1,0), (4, 0), (0, –3) 40. (–2, 0), (2, 0), (0, 3) 41. 2 y x   42. 6 y x   43. 2 8 y x  

  10. Page 10
    Read page 10 as text

    Chapter 1: Graphs 4 44. 3 9 y x   45. 2 1 y x   46. 2 9 y x   47. 2 4 y x    48. 2 1 y x    49. 2 3 6 x y   50. 5 2 10 x y  

  11. Page 11
    Read page 11 as text

    Section 1.1: Graphing Utilities; Introduction to Graphing Equations 5 51. 2 9 4 36 x y   52. 2 4 4 x y   53. 2 13 y x       The x-intercept is 6.5 x  and the y-intercept is 13 y   . 54. 3 14 y x        The x-intercept is 4.67 x  and the y-intercept is 14 y  . 55. 2 2 15 y x       The x-intercepts are 2.74 x   and 2.74 x  . The y-intercept is 15 y   . 56. 2 3 19 y x       

  12. Page 12
    Read page 12 as text

    Chapter 1: Graphs 6 The x-intercepts are 2.52 x   and 2.52 x  . The y-intercept is 19 y  . 57. 3 43 3 2 43 or 2 x x y y         The x-intercept is 14.33 x  and the y-intercept is 21.5 y   . 58. 4 82 4 5 82 or 5 x x y y          The x-intercept is 20.5 x  and the y-intercept is 16.4 y  . 59. 2 2 5 37 5 3 37 or 3 x x y y          The x-intercepts are 2.72 x   and 2.72 x  . The y-intercept is 12.33 y  . 60. 2 2 2 35 2 3 35 or 3 x x y y         The x-intercepts are 4.18 x   and 4.18 x  . The y-intercept is 11.67 y   . 61. If   2, 5 is shifted 3 units right then the x coordinate would be 2 3  . If it is shifted 2 units down then the y-coordinate would be 5 ( 2)   .

  13. Page 13
    Read page 13 as text

    Section 1.1: Graphing Utilities; Introduction to Graphing Equations 7 Thus the new point would be   2 3, 5 ( 2) (5,3)     . 62. If   1, 6  is shifted 2 units left then the x coordinate would be 1 ( 2)    . If it is shifted 4 units up then the y-coordinate would be 6 4  . Thus the new point would be   1 ( 2), 6 4 ( 3,10)       . 63. a. 25 feet b. 23.2 ft; 34.1 ft c. (0,6), The shot is released at a height of 6 feet; (48.7, 0), the shot hits the ground after traveling a horizontal distance of 48.7 feet. 64. a. 20 meters b. 12 seconds; 36 meters c. (0, 2), The discus is released at a height of 2 meters; (18, 0), the discus hits the ground after 18 seconds. 65. a. $19.95; $19.95 b. $182.45 c. (0, 19.95), The membership plan costs $19.95 per month. 66. a. 1.5 miles b. 1 mile c. (0, 2), Caleb’s friend lives 2 miles from his house; (28, 0), it takes Caleb 28 minutes to ride home. 67. ( 1, 0), (1, 0), (0, 1), (0,1)   68. ( 2, 0), (3, 0), (0, 2), (0, 0), (0, 2)   69. Answers will vary 70. a. b. Since 2 x x  for all x , the graphs of 2 and y x y x   are the same. c. For   2 y x  , the domain of the variable x is 0 x  ; for y x  , the domain of the variable x is all real numbers. Thus,   2 only for 0. x x x   d. For 2 y x  , the range of the variable y is 0 y  ; for y x  , the range of the variable y is all real numbers. Also, 2 only if 0. x x x   71. Answers will vary

  14. Page 14
    Read page 14 as text

    Chapter 1: Graphs 8 72. Answers will vary. A complete graph presents enough of the graph to the viewer so they can “see” the rest of the graph as an obvious continuation of what is shown. 73. Answers will vary. Section 1.2 1.   5 3 8 8     2. 2 2 3 4 25 5    3. 2 2 2 11 60 121 3600 3721 61      Since the sum of the squares of two of the sides of the triangle equals the square of the third side, the triangle is a right triangle. 4.   0, 0 5. 1 2 bh 6. true 7. midpoint 8. False; the distance between two points is never negative. 9. True; 1 2 1 2 , 2 2 x x y y M          10. a 11. 2 2 1 2 2 2 ( , ) (2 0) (1 0) 2 1 4 1 5 d P P          12. 2 2 1 2 2 2 ( , ) ( 2 0) (1 0) ( 2) 1 4 1 5 d P P            13. 2 2 1 2 2 2 ( , ) ( 2 1) (2 1) ( 3) 1 9 1 10 d P P            14.   2 2 1 2 2 2 ( , ) 2 ( 1) (2 1) 3 1 9 1 10 d P P           15.       2 2 1 2 2 2 ( , ) (5 3) 4 4 2 8 4 64 68 2 17 d P P            16.         2 2 1 2 2 2 ( , ) 2 1 4 0 3 4 9 16 25 5 d P P            17.   2 2 1 2 2 2 ( , ) 4 ( 7) (0 3) 11 ( 3) 121 9 130            d P P 18.     2 2 1 2 2 2 ( , ) 4 2 2 ( 3) 2 5 4 25 29 d P P           19.   2 2 1 2 2 2 ( , ) (6 5) 1 ( 2) 1 3 1 9 10           d P P 20.     2 2 1 2 2 2 ( , ) 6 ( 4) 2 ( 3) 10 5 100 25 125 5 5 d P P             21.     2 2 1 2 2 2 ( , ) 2.3 ( 0.2) 1.1 (0.3) 2.5 0.8 6.25 0.64 6.89 2.62            d P P 22.     2 2 1 2 2 2 ( , ) 0.3 1.2 1.1 2.3 ( 1.5) ( 1.2) 2.25 1.44 3.69 1.92              d P P 23. 2 2 1 2 2 2 2 2 ( , ) (0 ) (0 ) ( ) ( ) d P P a b a b a b           24. 2 2 1 2 2 2 2 2 2 ( , ) (0 ) (0 ) ( ) ( ) 2 2 d P P a a a a a a a a            

  15. Page 15
    Read page 15 as text

    Section 1.2: The Distance and Midpoint Formulas 9 25. ( 2,5), (1,3), ( 1, 0) A B C            2 2 2 2 2 2 2 2 2 2 2 2 ( , ) 1 ( 2) (3 5) 3 ( 2) 9 4 13 ( , ) 1 1 (0 3) ( 2) ( 3) 4 9 13 ( , ) 1 ( 2) (0 5) 1 ( 5) 1 25 26 d A B d B C d A C                                    Verifying that ∆ ABC is a right triangle by the Pythagorean Theorem:             2 2 2 2 2 2 ( , ) ( , ) ( , ) 13 13 26 13 13 26 26 26 d A B d B C d A C        The area of a triangle is 1 2 A bh   . In this problem,     1 ( , ) ( , ) 2 1 1 13 13 13 2 2 13 square units 2 A d A B d B C          26. ( 2, 5), (12, 3), (10, 11) A B C            2 2 2 2 2 2 2 2 2 2 2 2 ( , ) 12 ( 2) (3 5) 14 ( 2) 196 4 200 10 2 ( , ) 10 12 ( 11 3) ( 2) ( 14) 4 196 200 10 2 ( , ) 10 ( 2) ( 11 5) 12 ( 16) 144 256 400 20 d A B d B C d A C                                       Verifying that ∆ ABC is a right triangle by the Pythagorean Theorem:             2 2 2 2 2 2 ( , ) ( , ) ( , ) 10 2 10 2 20 200 200 400 400 400 d A B d B C d A C        The area of a triangle is 1 2 A bh  . In this problem,     1 ( , ) ( , ) 2 1 10 2 10 2 2 1 100 2 100 square units 2 A d A B d B C          

  16. Page 16
    Read page 16 as text

    Chapter 1: Graphs 10 27. ( 5,3), (6, 0), (5,5) A B C           2 2 2 2 2 2 2 2 2 2 2 2 ( , ) 6 ( 5) (0 3) 11 ( 3) 121 9 130 ( , ) 5 6 (5 0) ( 1) 5 1 25 26 ( , ) 5 ( 5) (5 3) 10 2 100 4 104 2 26 d A B d B C d A C                                 Verifying that ∆ ABC is a right triangle by the Pythagorean Theorem:             2 2 2 2 2 2 ( , ) ( , ) ( , ) 104 26 130 104 26 130 130 130 d A C d B C d A B        The area of a triangle is 1 2 A bh  . In this problem,     1 ( , ) ( , ) 2 1 104 26 2 1 2 26 26 2 1 2 26 2 26 square units A d A C d B C              28. ( 6, 3), (3, 5), ( 1, 5) A B C             2 2 2 2 2 2 2 2 2 2 2 2 ( , ) 3 ( 6) ( 5 3) 9 ( 8) 81 64 145 ( , ) 1 3 (5 ( 5)) ( 4) 10 16 100 116 2 29 ( , ) 1 ( 6) (5 3) 5 2 25 4 29 d A B d B C d A C                                     Verifying that ∆ ABC is a right triangle by the Pythagorean Theorem:             2 2 2 2 2 2 ( , ) ( , ) ( , ) 29 2 29 145 29 4 29 145 29 116 145 145 145 d A C d B C d A B           The area of a triangle is 1 2 A bh  . In this problem,     1 ( , ) ( , ) 2 1 29 2 29 2 1 2 29 2 29 square units A d A C d B C          

1576 more pages in the full document

Unlock it once and it stays in your library, ready to chat with or turn into flashcards.

Unlock the full document

More Mathematics study materials

See all

Study this document with CramX

Once it is in your library, every tool can work from it.