Solution Manual for College Algebra Enhanced with Graphing Utilities, 8th Edition

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

Table of Contents
Chapter R Review
R.1 Real Numbers ............................................................................................................................1
R.2 Algebra Essentials .....................................................................................................................5
R.3 Geometry Essentials ................................................................................................................11
R.4 Polynomials .............................................................................................................................16
R.5 Factoring Polynomials ............................................................................................................23
R.6 Synthetic Division ...................................................................................................................28
R.7 Rational Expressions ...............................................................................................................30
R.8 nth Roots; Rational Exponents ................................................................................................40
Chapter 1 Graphs, Equations, and Inequalities
1.1 Graphing Utilities; Introduction to Graphing Equations.........................................................50
1.2 Solving Equations Using a Graphing Utility; Linear and Rational Equations .......................57
1.3 Quadratic Equations ................................................................................................................71
1.4 Complex Numbers; Quadratic Equations in the Complex Number System ...........................90
1.5 Radical Equations; Equations Quadratic in Form; Absolute Value Equations;
Factorable Equations ...............................................................................................................96
1.6 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications......117
1.7 Solving Inequalities...............................................................................................................125
Chapter Review .............................................................................................................................137
Chapter Test...................................................................................................................................147
Chapter Projects .............................................................................................................................151
Chapter 2 Graphs
2.1 The Distance and Midpoint Formulas ...................................................................................152
2.2 Intercepts; Symmetry; Graphing Key Equations ..................................................................165
2.3 Lines ......................................................................................................................................182
2.4 Circles ...................................................................................................................................200
2.5 Variation................................................................................................................................215
Chapter Review .............................................................................................................................220
Chapter Test ...................................................................................................................................226
Cumulative Review .......................................................................................................................228
Chapter Projects .............................................................................................................................230
Chapter 3 Functions and Their Graphs
3.1 Functions ...............................................................................................................................231
3.2 The Graph of a Function .......................................................................................................249
3.3 Properties of Functions .........................................................................................................258
3.4 Library of Functions; Piecewise-defined Functions .............................................................275
3.5 Graphing Techniques: Transformations................................................................................287
3.6 Mathematical Models: Building Functions ...........................................................................305
Chapter Review .............................................................................................................................313
Chapter Test ...................................................................................................................................320
Cumulative Review .......................................................................................................................323
Chapter Projects.............................................................................................................................327

Chapter 4 Linear and Quadratic Functions
4.1 Properties of Linear Functions and Linear Models ...............................................................329
4.2 Building Linear Models from Data .......................................................................................340
4.3 Quadratic Functions and Their Properties ............................................................................346
4.4 Building Quadratic Models from Verbal Descriptions and from Data .................................370
4.5 Inequalities Involving Quadratic Functions ..........................................................................378
Chapter Review .............................................................................................................................397
Chapter Test ...................................................................................................................................405
Cumulative Review .......................................................................................................................408
Chapter Projects .............................................................................................................................411
Chapter 5 Polynomial and Rational Functions
5.1 Polynomial Functions ...........................................................................................................414
5.2 The Graph of a Polynomial Function; Models......................................................................425
5.3 The Real Zeros of a Polynomial Function ............................................................................445
5.4 Complex Zeros; Fundamental Theorem of Algebra .............................................................482
5.5 Properties of Rational Functions ...........................................................................................491
5.6 The Graph of a Rational Function.........................................................................................501
5.7 Polynomial and Rational Inequalities ...................................................................................557
Chapter Review .............................................................................................................................579
Chapter Test ...................................................................................................................................593
Cumulative Review .......................................................................................................................597
Chapter Projects .............................................................................................................................602
Chapter 6 Exponential and Logarithmic Functions
6.1 Composite Functions.............................................................................................................603
6.2 One-to-One Functions; Inverse Functions ............................................................................621
6.3 Exponential Functions...........................................................................................................644
6.4 Logarithmic Functions ..........................................................................................................665
6.5 Properties of Logarithms .......................................................................................................687
6.6 Logarithmic and Exponential Equations ...............................................................................696
6.7 Financial Models ...................................................................................................................717
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models .................................................................................................................725
6.9 Building Exponential, Logarithmic, and Logistic Models from Data ..................................736
Chapter Review .............................................................................................................................741
Chapter Test ...................................................................................................................................753
Cumulative Review .......................................................................................................................757
Chapter Projects .............................................................................................................................760

Chapter 7 Analytic Geometry
7.2 The Parabola .........................................................................................................................763
7.3 The Ellipse ............................................................................................................................778
7.4 The Hyperbola.......................................................................................................................796
Chapter Review .............................................................................................................................816
Chapter Test ...................................................................................................................................821
Cumulative Review .......................................................................................................................823
Chapter Projects .............................................................................................................................825
Chapter 8 Systems of Equations and Inequalities
8.1 Systems of Linear Equations: Substitution and Elimination ................................................828
8.2 Systems of Linear Equations: Matrices ................................................................................851
8.3 Systems of Linear Equations: Determinants .........................................................................876
8.4 Matrix Algebra ......................................................................................................................890
8.5 Partial Fraction Decomposition ............................................................................................909
8.6 Systems of Nonlinear Equations ...........................................................................................928
8.7 Systems of Inequalities .........................................................................................................956
8.8 Linear Programming .............................................................................................................971
Chapter Review .............................................................................................................................984
Chapter Test ...................................................................................................................................999
Cumulative Review .....................................................................................................................1008
Chapter Projects...........................................................................................................................1011
Chapter 9 Sequences; Induction; the Binomial Theorem
9.1 Sequences ............................................................................................................................1014
9.2 Arithmetic Sequences .........................................................................................................1028
9.3 Geometric Sequences; Geometric Series ............................................................................1037
9.4 Mathematical Induction ......................................................................................................1048
9.5 The Binomial Theorem .......................................................................................................1057
Chapter Review ...........................................................................................................................1064
Chapter Test .................................................................................................................................1068
Cumulative Review .....................................................................................................................1071
Chapter Projects ...........................................................................................................................1073
Chapter 10 Counting and Probability
10.1 Counting ..............................................................................................................................1076
10.2 Permutations and Combinations .........................................................................................1079
10.3 Probability ...........................................................................................................................1084
Chapter Review ...........................................................................................................................1091
Chapter Test .................................................................................................................................1093
Cumulative Review .....................................................................................................................1094
Chapter Projects ...........................................................................................................................1097

1
Chapter R
Review
Section R.1
1. rational
2. 4 5 6 3 4 30 3 31      
3. Distributive
4. c
5. a
6. b
7. True
8. False; The Zero-Product Property states that if a
product equals 0, then at least one of the factors
must equal 0.
9. False; 6 is the Greatest Common Factor of 12
and 18. The Least Common Multiple is the
smallest value that both numbers will divide
evenly. The LCM for 12 and 18 is 36.
10. True
11.    
 
1, 3, 4,5, 9 2, 4, 6, 7,8
1, 2,3, 4, 5, 6, 7,8, 9
A B  

12.    
 
1, 3, 4,5, 9 1, 3, 4, 6
1, 3, 4, 5, 6, 9
A C  

13.      1, 3, 4,5, 9 2, 4, 6, 7,8 4A B   
14.      1, 3, 4,5, 9 1, 3, 4, 6 1, 3, 4A C   
15.
      
   
 
( )
1, 3, 4,5, 9 2, 4, 6, 7,8 1,3, 4, 6
1, 2,3, 4,5, 6, 7,8,9 1,3, 4, 6
1, 3, 4, 6
A B C 
  
 

16.
      
   
 
( )
1, 3, 4,5, 9 2, 4, 6, 7,8 1,3, 4, 6
4 1, 3, 4, 6
1,3, 4, 6
 
  
 

A B C
17.  0, 2, 6, 7, 8A 
18.  0, 2, 5, 7, 8, 9C 
19.    
   
1, 3, 4, 5, 9 2, 4, 6, 7, 8
4 0, 1, 2, 3, 5, 6, 7, 8, 9
A B  
 
20.    
   
2, 4, 6, 7, 8 1, 3, 4, 6
1, 2, 3, 4, 6, 7, 8 0, 5, 9
B C  
 
21.    
 
0, 2, 6, 7, 8 0, 1, 3, 5, 9
0, 1, 2, 3, 5, 6, 7, 8, 9
A B  

22.    
 
0, 1, 3, 5, 9 0, 2, 5, 7, 8, 9
0, 5, 9
B C  

23. a.  2,5
b.  6, 2,5
c.  1
6, , 1.333... 1.3, 2,5
2
   
d.  

e.  1
6, , 1.333... 1.3, , 2,5
2
   
24. a.  1
b.  0,1
c.  5 , 2.060606... 2.06,1.25, 0,1
3
 
d.  5

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Chapter R: Review
2
e.  5 , 2.060606... 2.06,1.25, 0,1, 5
3
 
25. a.  1
b.  0,1
c.  1 1 1
0,1, , ,
2 3 4
d. None
e.  1 1 1
0,1, , ,
2 3 4
26. a. None
b.  1
c.  1.3, 1.2, 1.1, 1   
d. None
e.  1.3, 1.2, 1.1, 1   
27. a. None
b. None
c. None
d.  1
2, , 2 1, 2

 
e.  1
2, , 2 1, 2

 
28. a. None
b. None
c.  1 10.3
2 
d.  2, 2
 
e.  1
2, 2, 10.3
2
  
29. a. 18.953 b. 18.952
30. a. 25.861 b. 25.861
31. a. 28.653 b. 28.653
32. a. 99.052 b. 99.052
33. a. 0.063 b. 0.062
34. a. 0.054 b. 0.053
35. a. 9.999 b. 9.998
36. a. 1.001 b. 1.000
37. a. 0.429 b. 0.428
38. a. 0.556 b. 0.555
39. a. 34.733 b. 34.733
40. a. 16.200 b. 16.200
41. 3 2 5 
42. 5 2 10 
43. 2 3 4x   
44. 3 2 2y  
45. 3 1 2y  
46. 2 4 6x  
47. 2 6x  
48. 2 6y 
49. 6
2
x 
50. 2 6
x 
51. 9 4 2 5 2 7    
52. 6 4 3 2 3 5    
53. 6 4 3 6 12 6      
54. 8 4 2 8 8 0    
55. 18 5 2 18 10 8    
56. 100 10 2 100 20 80    
57. 1 12 1 13
4 3 3 3

  
58. 1 4 1 3
2 2 2 2

  

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Section R.1: Real Numbers
3
59.    6 3 5 2 3 2 6 15 2 1
6 17
11
              
 
 
60.    
 
 
2 8 3 4 2 3 2 8 3 6 3
2 8 18 3
2 10 3
20 3
23
               
   
   
  
 
61.    4 9 5 6 7 3 4 14 42 3
56 42 3
14 3
17
        
  
 

62.    1 4 3 2 2 1 12 2 2
1 12
11
       
 
 
63.    
 
 
10 6 2 2 8 3 2 10 6 4 5 2
10 2 5 2
10 7 2
10 14
4
            
   
  
 
 
64.    
 
2 5 4 6 3 4 2 20 6 1
18 6
18 6
12
               
   
  
 
65.    
1 1
5 3 2 1
2 2
  
66.    1 1
5 4 9 3
3 3
  
67. 4 8 12 6
5 3 2
  

68. 2 4

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Section R.2: Algebra Essentials
5
108. Subtraction is not associative; for
example:    5 2 1 2 4 5 2 1       .
109. Division is not commutative; for example:
2 3
3 2
 .
110. Division is not associative; for
example:  12 2 2 6 2 3     , but
 12 2 2 12 1 12     .
111. The Symmetric Property implies that if 2 = x,
then x = 2.
112. From the principle of substitution, if 5x  , then
     
2
2
2
5 5
25
25 5
30
x x
x
x x
x x

 
   
  
113. There are no real numbers that are both rational
and irrational, since an irrational number, by
definition, is a number that cannot be expressed
as the ratio of two integers; that is, not a rational
number
Every real number is either a rational number or
an irrational number, since the decimal form of a
real number either involves an infinitely
repeating pattern of digits or an infinite, non-
repeating string of digits.
114. The sum of an irrational number and a rational
number must be irrational. Otherwise, the
irrational number would then be the difference of
two rational numbers, and therefore would have
to be rational.
115. Answers will vary.
116. Since 1 day = 24 hours, we compute
12997 541.5416
24  .
Now we only need to consider the decimal part
of the answer in terms of a 24 hour day. That is,
  0.5416 24 13 hours. So it must be 13 hours
later than 12 noon, which makes the time 1 AM
CST.
117. Answers will vary.
Section R.2
1. variable
2. origin
3. strict
4. base; exponent (or power)
5. 3
1.2345678 10
6. d
7. a
8. b
9. True
10. False; the absolute value of a real number is
nonnegative. 0 0 which is not a positive
number.
11. False; a number in scientific notation is
expressed as the product of a number, x,
1 10x  or 10 1x    , and a power of 10.
12. True
13.
  5
2

 3
4
14. 1
3
3
2
  
2
3
15. 1 0
2 
16. 5 6
17. 1 2  
18. 5
3 2
  
19. 3.14 
20. 2 1.41

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Chapter R: Review
6
21. 1 0.5
2 
22. 1 0.33
3 
23. 2 0.67
3 
24. 1 0.25
4 
25. 0x 
26. 0z 
27. 2x 
28. 5y  
29. 1x 
30. 2x 
31. Graph on the number line: 2x  

32. Graph on the number line: 4x 

33. Graph on the number line: 1x  
 
34. Graph on the number line: 7x 
 
35. ( , ) (0,1) 1 0 1 1d C D d    
36. ( , ) (0, 3) 3 0 3 3d C A d       
37. ( , ) (1,3) 3 1 2 2d D E d    
38. ( , ) (0,3) 3 0 3 3d C E d    
39. ( , ) ( 3,3) 3 ( 3) 6 6d A E d      
40. ( , ) (1, 1) 1 1 2 2d D B d       
41. 2 2 2 3 2 6 4x y        
42. 3 3( 2) 3 6 3 3x y        
43. 5 2 5( 2)(3) 2 30 2 28xy         
44. 2 2( 2) ( 2)(3) 4 6 2x xy          
45. 2( 2) 42 4
2 3 5 5
x
x y
 
  
   
46. 2 3 1 1
2 3 5 5
x y
x y
     
   
47. 3( 2) 2(3) 6 63 2 0 0
2 2 3 5 5
x y
y
       
 
48. 2( 2) 3 4 32 3 7
3 3 3
x
y
       
49. 3 ( 2) 1 1x y     
50. 3 ( 2) 5 5x y     
51. 3 2 3 2 5x y      
52. 3 2 3 2 1x y      
53. 3 3 1
3 3
x
x   
54. 2 2 1
2 2
y
y

   
 
55. 4 5 4(3) 5( 2)
12 10
22
22
x y   
 


56. 3 2 3(3) 2( 2) 9 4 5 5x y      

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Section R.2: Algebra Essentials
7
58. 3 2 3 3 2 2
3 3 2 2
9 4
13
x y   
   
 

59.
2 1x
x

Part (c) must be excluded. The value 0x  must
be excluded from the domain because it causes
division by 0.
60.
2 1x
x

Part (c) must be excluded. The value 0x  must
be excluded from the domain because it causes
division by 0.
61. 2 ( 3)( 3)9
x x
x xx   
Part (a) , 3x  , must be excluded because it
causes the denominator to be 0.
62. 2 9
x
x 
None of the given values are excluded. The
domain is all real numbers.
63.
2
2 1
x
x 
None of the given values are excluded. The
domain is all real numbers.
64.
3 3
2 ( 1)( 1)1
x x
x xx   
Parts (b) and (d) must be excluded. The values
1, and 1x x   must be excluded from the
domain because they cause division by 0.
65.
2 2
3
5 10 5 10
( 1)( 1)
x x x x
x x xx x
   
  
Parts (b), (c), and (d) must be excluded. The
values 0, 1, and 1x x x    must be excluded
from the domain because they cause division by
0.
66.
2 2
3 2
9 1 9 1
( 1)
x x x x
x x x x
     

 
Part (c) must be excluded. The value 0x  must
be excluded from the domain because it causes
division by 0.
67. 4
5x 
5x  must be exluded because it makes the
denominator equal 0.
 Domain 5x x 
68. 6
4x


4x   must be excluded sine it makes the
denominator equal 0.
 Domain 4x x  
69. 4
x
x 
4x   must be excluded sine it makes the
denominator equal 0.
 Domain 4x x  
70. 2
6
x
x


6x  must be excluded sine it makes the
denominator equal 0.
 Domain 6x x 
71. 5 5 5
( 32) (32 32) (0) 0 C
9 9 9
C F      
72. 5 5 5
( 32) (212 32) (180) 100 C
9 9 9
C F      
73. 5 5 5
( 32) (77 32) (45) 25 C
9 9 9
C F      
74. 5 5
( 32) ( 4 32)
9 9
5 ( 36)
9
20 C
C F    
 
  
75. 2
( 9) ( 9)( 9) 81    
76. 2 2
4 (4) 16    
77. 2
2
1 1
4 164
  

Loading page 12...

Chapter R: Review
8
78. 2
2
1 1
4 164

    
79. 6 4 6 4 2
2
1 1
3 3 3 3 93
   
    
80. 2 3 2 3 1
4 4 4 4 4  
   
81.     1 3 13 3
4 4 4 64
     
82.     3 1 31 3
2 2 2 8
     
83. 2
100 10 10 
84. 2
36 6 6 
85.  2
4 4 4   
86.  2
3 3 3   
87.    
2 24 2 4 8
9 9 81 x x x
88.   12
2 2
1 1
4 4 4
x x x

   

89.       42 2 22 1 2 1 4 2
2
x
x y x y x y y
  
   
90.     33 31 1 3 3 3
3
y
x y x y x y x
  
   
91.
2 5 2 3 5 4 1 1
3 4
  
  
x y y
x y x y xx y
92.
2 2 1 1 2 3 1
2 3
1x y x y x y
x y x y
     
  

Loading page 13...

Section R.2: Algebra Essentials
9
108.  2
1 1x
y   
109. If 2,x 
3 2 3 2
2 3 5 4 2 2 3 2 5 2 4
16 12 10 4
10
x x x         
   

If 1,x 
3 2 3 2
2 3 5 4 2 1 3 1 5 1 4
2 3 5 4
0
x x x         
   

110. If 1,x 
3 2 3 2
4 3 2 4 1 3 1 1 2
4 3 1 2
8
x x x        
   

If 2,x 
3 2 3 2
4 3 2 4 2 3 2 2 2
32 12 2 2
44
x x x        
   

111.
44 4
4
(666) 666 3 81
222(222)
 
   
 
112.  
3 33 3
3 3
3
3
1
(0.1) (20) 2 10
10
1 2 10
10
2 8
 
   
 
  
 
113. 6
(8.2) 304, 006.671
114. 5
(3.7) 693.440
115. 3
(6.1) 0.004 
116. 5
(2.2) 0.019 
117. 6
( 2.8) 481.890 
118. 6
(2.8) 481.890  
119. 4
( 8.11) 0.000
 
120. 4
(8.11) 0.000
  
121. 2
454.2 4.542 10 
122. 1
32.14 3.214 10 
123. 2
0.013 1.3 10
 
124. 3
0.00421 4.21 10
 
125. 4
32,155 3.2155 10 
126. 4
21, 210 2.121 10 
127. 4
0.000423 4.23 10
 
128. 2
0.0514 5.14 10
 
129. 4
6.15 10 61,500 
130. 3
9.7 10 9700 
131. 3
1.214 10 0.001214
 
132. 4
9.88 10 0.000988
 
133. 8
1.1 10 110, 000, 000 
134. 2
4.112 10 411.2 
135. 2
8.1 10 0.081
 
136. 1
6.453 10 0.6453
 
137. A lw
138.  2P l w 
139. C d

140. 1
2
A bh
141. 23
4
A x
142. 3P x
143. 34
3
V r


Loading page 14...

Chapter R: Review
10
144. 2
4S r

145. 3
V x
146. 2
6S x
147. a. If 1000,x 
4000 2
4000 2(1000)
4000 2000
$6000
C x 
 
 

The cost of producing 1000 watches is
$6000.
b. If 2000,x 
4000 2
4000 2(2000)
4000 4000
$8000
C x 
 
 

The cost of producing 2000 watches is
$8000.
148. 210 80 120 25 60 32 5 $98      
His balance at the end of the month was $98.
149. We want the difference between x and 4 to be at
least 6 units. Since we don’t care whether the
value for x is larger or smaller than 4, we take
the absolute value of the difference. We want the
inequality to be non-strict since we are dealing
with an ‘at least’ situation. Thus, we have
4 6x  
150. We want the difference between x and 2 to be
more than 5 units. Since we don’t care whether
the value for x is larger or smaller than 2, we
take the absolute value of the difference. We
want the inequality to be strict since we are
dealing with a ‘more than’ situation. Thus, we
have
2 5x  
151. a. 110 108 110 2 2 5x       
108 volts is acceptable.
b. 110 104 110 6 6 5x       
104 volts is not acceptable.
152. a. 220 214 220 6 6 8x       
214 volts is acceptable.
b. 220 209 220 11 11 8x       
209 volts is not acceptable.
153. a. 3 2.999 3
0.001
0.001 0.01
x   
 
 
A radius of 2.999 centimeters is acceptable.
b. 3 2.89 3
0.11
0.11 0.01
x   
 
 
A radius of 2.89 centimeters is not
acceptable.
154. a. 98.6 97 98.6
1.6
1.6 1.5
x   
 
 
97˚F is unhealthy.
b. 98.6 100 98.6
1.4
1.4 1.5
x   

 
100˚F is not unhealthy.
155. The distance from Earth to the Moon is about
8
4 10 400, 000, 000  meters.
156. The height of Mt. Everest is about
3
8848 8.848 10  meters.
157. The wavelength of visible light is about
7
5 10 0.0000005
  meters.
158. The diameter of an atom is about
10
1 10 0.0000000001
  meters.
159. The diameter is about 2
0.0403 4.03 10
 
inches.
160. The tiniest motor is less than 5
0.00004 4 10
 
millimeters tall.

Loading page 15...

Section R.3: Geometry Essentials
11
161.
     5 1 1 2
2
1.86 10 6 10 2.4 10 3.65 10
186, 000 60 60 24 365
   
   

10 12
586.5696 10 5.865696 10   
There are about 12
5.9 10 miles in one light-
year.
162.
7 2
5
93, 000, 000 9.3 10 5 10
186, 000 1.86 10
500 seconds 8 min. 20 sec.

  

 
It takes about 8 minutes 20 seconds for a beam
of light to reach Earth from the Sun.
163. 1 0.333333 ... 0.333
3  
1
3 is larger by approximately 0.0003333 ...
164. 2
3 0.666666 ... 0.666 
2
3 is larger by approximately 0.000666 ...
165.   6 13 19
20
5.24 10 6.5 10 34.06 10
3.406 10
   
 
166.
4 4 6
10 10
5
1.62 10 1.62 10 0.36 10
4.54.5 10 10
3.6 10
 
 
    

 
167. No. For any positive number a, the value 2
a is
smaller and therefore closer to 0.
168. We are given that 2
1 10x  . This implies that
1 10x  . Since 10 3.162x   and
3.142x
  , the number could be 3.15 or 3.16
(which are between 1 and 10 as required). The
number could also be 3.14 since numbers such as
3.146 which lie between
 and 10 would
equal 3.14 when truncated to two decimal places.
169. Answers will vary.
170. Answers will vary.
5 < 8 is a true statement because 5 is further to
the left than 8 on a real number line.
Section R.3
1. right; hypotenuse
2. 1
2
A bh
3. 2C r

4. similar
5. c
6. b
7. True.
8. True. 2 2 2
6 8 36 64 100 10    
9. False; the surface area of a sphere of radius r is
given by 2
4V r
 .
10. True. The lengths of the corresponding sides are
equal.
11. True. Two corresponding angles are equal.
12. False. The sides are not proportional.
13.
2 2 2
2 2
5, 12,
5 12
25 144
169 13
a b
c a b
c
 
 
 
 
  
14.
2 2 2
2 2
6, 8,
6 8
36 64
100 10
a b
c a b
c
 
 
 
 
  
15.
2 2 2
2 2
10, 24,
10 24
100 576
676 26
a b
c a b
c
 
 
 
 
  
16.
2 2 2
2 2
4, 3,
4 3
16 9
25 5
a b
c a b
c
 
 
 
 
  

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Solution Manual for College Algebra Enhanced with Graphing Utilities, 8th Edition

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