SOLUTIONS
MANUAL
T IM B RITT
Jackson State Community College
P RECALCULUS
E NHANCED WITH G RAPHING U TILITIES
EIGHTH EDITION
Michael Sullivan
Chicago State University
Michael Sullivan III
Joliet Junior College

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

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

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

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 nth Roots; Rational Exponents .......................................................................................... 1572
Appendix B: The Limit of a Sequence; Infinite Series.................................................... 1583

Loading page 6...

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

Loading page 7...

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

Loading page 8...

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 2y 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 9y 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 1y 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 4x y 
2 2
0 2 4
4 4
 

2 2
( 2) 2 4
8

Loading page 9...

Loading page 10...

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

Loading page 11...

Chapter 1: Graphs
6
The x-intercepts are 2.52x   and 2.52x  .
The y-intercept is 19y  .
57. 3 43
3 2 43 or 2
x
x y y 
  

 

The x-intercept is 14.33x  and the y-intercept
is 21.5y   .
58. 4 82
4 5 82 or 5
x
x y y  
  



The x-intercept is 20.5x  and the y-intercept is
16.4y  .
59.
2
2 5 37
5 3 37 or 3
x
x y y  
  



The x-intercepts are 2.72x   and 2.72x  .
The y-intercept is 12.33y  .
60.
2
2 2 35
2 3 35 or 3
x
x y y 
  



The x-intercepts are 4.18x   and 4.18x  .
The y-intercept is 11.67y   .
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)  .

Loading page 12...

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 andy x y x  are the same.
c. For  2
y x , the domain of the variable
x is 0x  ; 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
0y  ; 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

Loading page 13...

Loading page 14...

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
1 113 13 13
2 2
13 square units2
A d A B d B C 
  

Loading page 15...

Loading page 16...

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

Study Now!

Document Details

Related Documents

Test Bank For Precalculus, 11th Edition

Solution Manual for Precalculus, 8th Edition

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

Precalculus Enhanced with Graphing Utilities 4th Edition Solution Manual

Solution Manual for Precalculus, 11th Edition

Solution Manual for Precalculus , 10th Edition

Test Bank for Precalculus , 10th Edition

Test Bank for Precalculus Enhanced with Graphing Utilities , 7th Edition

Test Bank for Precalculus Enhanced with Graphing Utilities, 6th Edition

AP Calculus AB Scoring Guide Unit 6 Progress Check

Company

Explore

Study Tools