CONTENTS
Part I Solutions to All Exercises .................................................................... 1
Chapter P Prerequisites............................................................................................ 1
Chapter 1 Equations, Inequalities, and Mathematical Modeling ........................ 50
Chapter 2 Functions and Their Graphs............................................................... 163
Chapter 3 Polynomial Functions ........................................................................ 256
Chapter 4 Rational Functions and Conics .......................................................... 351
Chapter 5 Exponential and Logarithmic Functions ........................................... 432
Chapter 6 Systems of Equations and Inequalities .............................................. 502
Chapter 7 Matrices and Determinants ................................................................ 615
Chapter 8 Sequences, Series, and Probability .................................................... 711
Appendix A Errors and the Algebra of Calculus ................................................... 792
Solutions to Checkpoints ................................................................. 799
Solutions to Practice Tests .............................................................. 942
Part II Solutions to Chapter and Cumulative Tests................................. 962
,
, CHAPTER P
Prerequisites
Section P.1 Review of Real Numbers and Their Properties..................................... 2
Section P.2 Exponents and Radicals ......................................................................... 5
Section P.3 Polynomials and Special Products ....................................................... 10
Section P.4 Factoring Polynomials..........................................................................16
Section P.5 Rational Expressions ............................................................................23
Section P.6 The Rectangular Coordinate System and Graphs ............................... 32
Review Exercises ..........................................................................................................38
Problem Solving ...........................................................................................................45
Practice Test ...............................................................................................................49
© 2022 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
, C H A P T E R P
Prerequisites
Section P.1 Review of Real Numbers and Their Properties
1. irrational 10. 25, −17, − 12 , 9, 3.12, 12 π , 18, −11.1, 13
5
2. origin (a) Natural numbers: 25, 9 = 3, 18, 13
3. terms (b) Whole numbers: 25, 9 = 3, 18, 13
4. Zero-Factor Property (c) Integers: 25, −17, 9 = 3, 18, 13
5. Yes. 3 − 10 = −7 = 7 and 10 − 3 = 7 = 7. (d) Rational numbers: 25, −17, − 12
5
, 9 = 3,
3.12, 18, −11.1, 13
6. (a) iii
(b) iv (e) Irrational numbers: 12 π
(c) ii
(d) v 11. −4 > −8
(e) i
7. −9, − 72 , 5, 23 , 3, 0, 3, − 4, 2, −11 12. 1 < 16
3
(a) Natural numbers: 5, 8, 2
(b) Whole numbers: 5, 0, 8, 2
(c) Integers: −9, 5, 0, 8, − 4, 2, −11
5 2
13. 6
> 3
(d) Rational numbers: −9, − 72 , 5, 23 , 0, 8, − 4, 2, −11
(e) Irrational numbers: 3
8. 5, − 7, − 73 , 0, 3.14, 54 , − 3, 12, 5 14. − 87 < − 73
(a) Natural numbers: 12, 5
(b) Whole numbers: 0, 12, 5
(c) Integers: −7, 0, − 3, 12, 5
15. −5.2 > −8.5
(d) Rational numbers: −7, − 73 , 0, 3.14, 5
4
, − 3, 12, 5
(e) Irrational numbers: 5
16. − 43 > − 4.75
9. 2.01, 0.6, −13, 0.010110111 . . ., 1, − 6
(a) Natural numbers: 1
(b) Whole numbers: 1
(c) Integers: −13, 1, − 6 17. The inequality x ≤ 5 denotes the set of all real
numbers less than or equal to 5.
(d) Rational numbers: 2.01, 0.6, −13, 1, − 6
18. The inequality x < 0 denotes the set of all real
(e) Irrational numbers: 0.010110111 . . .
numbers less than zero.
2 © 2022 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Part I Solutions to All Exercises .................................................................... 1
Chapter P Prerequisites............................................................................................ 1
Chapter 1 Equations, Inequalities, and Mathematical Modeling ........................ 50
Chapter 2 Functions and Their Graphs............................................................... 163
Chapter 3 Polynomial Functions ........................................................................ 256
Chapter 4 Rational Functions and Conics .......................................................... 351
Chapter 5 Exponential and Logarithmic Functions ........................................... 432
Chapter 6 Systems of Equations and Inequalities .............................................. 502
Chapter 7 Matrices and Determinants ................................................................ 615
Chapter 8 Sequences, Series, and Probability .................................................... 711
Appendix A Errors and the Algebra of Calculus ................................................... 792
Solutions to Checkpoints ................................................................. 799
Solutions to Practice Tests .............................................................. 942
Part II Solutions to Chapter and Cumulative Tests................................. 962
,
, CHAPTER P
Prerequisites
Section P.1 Review of Real Numbers and Their Properties..................................... 2
Section P.2 Exponents and Radicals ......................................................................... 5
Section P.3 Polynomials and Special Products ....................................................... 10
Section P.4 Factoring Polynomials..........................................................................16
Section P.5 Rational Expressions ............................................................................23
Section P.6 The Rectangular Coordinate System and Graphs ............................... 32
Review Exercises ..........................................................................................................38
Problem Solving ...........................................................................................................45
Practice Test ...............................................................................................................49
© 2022 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
, C H A P T E R P
Prerequisites
Section P.1 Review of Real Numbers and Their Properties
1. irrational 10. 25, −17, − 12 , 9, 3.12, 12 π , 18, −11.1, 13
5
2. origin (a) Natural numbers: 25, 9 = 3, 18, 13
3. terms (b) Whole numbers: 25, 9 = 3, 18, 13
4. Zero-Factor Property (c) Integers: 25, −17, 9 = 3, 18, 13
5. Yes. 3 − 10 = −7 = 7 and 10 − 3 = 7 = 7. (d) Rational numbers: 25, −17, − 12
5
, 9 = 3,
3.12, 18, −11.1, 13
6. (a) iii
(b) iv (e) Irrational numbers: 12 π
(c) ii
(d) v 11. −4 > −8
(e) i
7. −9, − 72 , 5, 23 , 3, 0, 3, − 4, 2, −11 12. 1 < 16
3
(a) Natural numbers: 5, 8, 2
(b) Whole numbers: 5, 0, 8, 2
(c) Integers: −9, 5, 0, 8, − 4, 2, −11
5 2
13. 6
> 3
(d) Rational numbers: −9, − 72 , 5, 23 , 0, 8, − 4, 2, −11
(e) Irrational numbers: 3
8. 5, − 7, − 73 , 0, 3.14, 54 , − 3, 12, 5 14. − 87 < − 73
(a) Natural numbers: 12, 5
(b) Whole numbers: 0, 12, 5
(c) Integers: −7, 0, − 3, 12, 5
15. −5.2 > −8.5
(d) Rational numbers: −7, − 73 , 0, 3.14, 5
4
, − 3, 12, 5
(e) Irrational numbers: 5
16. − 43 > − 4.75
9. 2.01, 0.6, −13, 0.010110111 . . ., 1, − 6
(a) Natural numbers: 1
(b) Whole numbers: 1
(c) Integers: −13, 1, − 6 17. The inequality x ≤ 5 denotes the set of all real
numbers less than or equal to 5.
(d) Rational numbers: 2.01, 0.6, −13, 1, − 6
18. The inequality x < 0 denotes the set of all real
(e) Irrational numbers: 0.010110111 . . .
numbers less than zero.
2 © 2022 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
