All Chapters Covered
SOLUTION MANUAL
, CONTENTS
Part I Solutions to All Exercises..................................................................... 1
Chapter 1 Functions and Their Graphs................................................................... 1
Chapter 2 Polynomial and Rational Functions.....................................................60
Chapter 3 Exponential and Logarithmic Functions ...........................................123
Chapter 4 Trigonometry......................................................................................157
Chapter 5 Analytic Trigonometry.......................................................................205
Chapter 6 Additional Topics in Trigonometry ...................................................244
Chapter 7 Systems of Equations and Inequalities ..............................................287
Chapter 8 Matrices and Determinants ................................................................338
Chapter 9 Sequences, Series, and Probability ....................................................389
Chapter 10 Topics in Analytic Geometry.............................................................427
Chapter 11 Analytic Geometry in Three Dimensions..........................................501
Chapter 12 Limits and an Introduction to Calculus .............................................526
Appendix A Review of Fundamental Concepts of Algebra ..................................557
Solutions to Checkpoints .................................................................581
Solutions to Practice Tests...............................................................786
Part II Solutions to Chapter and Cumulative Tests .................................812
iii
Copyright 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
, C H A P T E R 1
Functions and Their Graphs
Section 1.1 Rectangular Coordinates ........................................................................2
Section 1.2 Graphs of Equations ...............................................................................5
Section 1.3 Linear Equations in Two Variables .....................................................10
Section 1.4 Functions...............................................................................................16
Section 1.5 Analyzing Graphs of Functions ...........................................................20
Section 1.6 A Library of Parent Functions .............................................................25
Section 1.7 Transformations of Functions ..............................................................28
Section 1.8 Combinations of Functions: Composite Functions.............................33
Section 1.9 Inverse Functions..................................................................................37
Section 1.10 Mathematical Modeling and Variation................................................44
Review Exercises ..........................................................................................................47
Problem Solving ...........................................................................................................55
Practice Test ...............................................................................................................58
Copyright 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
, C H A P T E R 1
Functions and Their Graphs
Section 1.1 Rectangular Coordinates
1. Cartesian
( x2 − x1 ) + ( y2 − y1 )
2 2
17. d =
3. Distance Formula
(3 − (−2)) + (−6 − 6)
2 2
=
5.
= (5)2 + ( −12)
2
= 25 + 144
= 13 units
19. d = ( x2 − x1 ) + ( y2 − y1 )
2 2
(−5 − 1) + ( −1 − 4)
2 2
=
= (−6)2 + ( −5)
2
7. ( − 3, 4)
= 36 + 25
9. x > 0 and y < 0 in Quadrant IV. = 61 units
11. x = −4 and y > 0 in Quadrant II.
21. d = ( x2 − x1 ) + ( y2 − y1 )
2 2
13. ( x, − y ) is in the second Quadrant means that ( x, y ) is
⎛ 1⎞ ⎛
2
4⎞
2
= ⎜ 2 − ⎟ + ⎜ −1 − ⎟
in Quadrant III. ⎝ 2 ⎠ ⎝ 3⎠
2 2
15. ⎛ 3⎞ ⎛ 7⎞
Year, x Number of Stores, y = ⎜ ⎟ + ⎜− ⎟
⎝ ⎠
2 ⎝ 3⎠
2003 4906
9 49
2004 5289 = +
4 9
2005 6141 277
=
36
2006 6779
277
2007 7262 = units
6
2008 7720
23. (a) (1, 0), (13, 5)
2009 8416
2010 8970
Distance = (13 − 1)2 + ( 5 − 0)
2
= 122 + 52 = 169 = 13
(13, 5), (13, 0)
Distance = 5 − 0 = 5 = 5
(1, 0), (13, 0)
Distance = 1 − 13 = −12 = 12
(b) 52 + 122 = 25 + 144 = 169 = 132
Year (t = 3 ↔ 2003)
2
Copyright 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
SOLUTION MANUAL
, CONTENTS
Part I Solutions to All Exercises..................................................................... 1
Chapter 1 Functions and Their Graphs................................................................... 1
Chapter 2 Polynomial and Rational Functions.....................................................60
Chapter 3 Exponential and Logarithmic Functions ...........................................123
Chapter 4 Trigonometry......................................................................................157
Chapter 5 Analytic Trigonometry.......................................................................205
Chapter 6 Additional Topics in Trigonometry ...................................................244
Chapter 7 Systems of Equations and Inequalities ..............................................287
Chapter 8 Matrices and Determinants ................................................................338
Chapter 9 Sequences, Series, and Probability ....................................................389
Chapter 10 Topics in Analytic Geometry.............................................................427
Chapter 11 Analytic Geometry in Three Dimensions..........................................501
Chapter 12 Limits and an Introduction to Calculus .............................................526
Appendix A Review of Fundamental Concepts of Algebra ..................................557
Solutions to Checkpoints .................................................................581
Solutions to Practice Tests...............................................................786
Part II Solutions to Chapter and Cumulative Tests .................................812
iii
Copyright 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
, C H A P T E R 1
Functions and Their Graphs
Section 1.1 Rectangular Coordinates ........................................................................2
Section 1.2 Graphs of Equations ...............................................................................5
Section 1.3 Linear Equations in Two Variables .....................................................10
Section 1.4 Functions...............................................................................................16
Section 1.5 Analyzing Graphs of Functions ...........................................................20
Section 1.6 A Library of Parent Functions .............................................................25
Section 1.7 Transformations of Functions ..............................................................28
Section 1.8 Combinations of Functions: Composite Functions.............................33
Section 1.9 Inverse Functions..................................................................................37
Section 1.10 Mathematical Modeling and Variation................................................44
Review Exercises ..........................................................................................................47
Problem Solving ...........................................................................................................55
Practice Test ...............................................................................................................58
Copyright 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
, C H A P T E R 1
Functions and Their Graphs
Section 1.1 Rectangular Coordinates
1. Cartesian
( x2 − x1 ) + ( y2 − y1 )
2 2
17. d =
3. Distance Formula
(3 − (−2)) + (−6 − 6)
2 2
=
5.
= (5)2 + ( −12)
2
= 25 + 144
= 13 units
19. d = ( x2 − x1 ) + ( y2 − y1 )
2 2
(−5 − 1) + ( −1 − 4)
2 2
=
= (−6)2 + ( −5)
2
7. ( − 3, 4)
= 36 + 25
9. x > 0 and y < 0 in Quadrant IV. = 61 units
11. x = −4 and y > 0 in Quadrant II.
21. d = ( x2 − x1 ) + ( y2 − y1 )
2 2
13. ( x, − y ) is in the second Quadrant means that ( x, y ) is
⎛ 1⎞ ⎛
2
4⎞
2
= ⎜ 2 − ⎟ + ⎜ −1 − ⎟
in Quadrant III. ⎝ 2 ⎠ ⎝ 3⎠
2 2
15. ⎛ 3⎞ ⎛ 7⎞
Year, x Number of Stores, y = ⎜ ⎟ + ⎜− ⎟
⎝ ⎠
2 ⎝ 3⎠
2003 4906
9 49
2004 5289 = +
4 9
2005 6141 277
=
36
2006 6779
277
2007 7262 = units
6
2008 7720
23. (a) (1, 0), (13, 5)
2009 8416
2010 8970
Distance = (13 − 1)2 + ( 5 − 0)
2
= 122 + 52 = 169 = 13
(13, 5), (13, 0)
Distance = 5 − 0 = 5 = 5
(1, 0), (13, 0)
Distance = 1 − 13 = −12 = 12
(b) 52 + 122 = 25 + 144 = 169 = 132
Year (t = 3 ↔ 2003)
2
Copyright 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
