This is the Student Solutions Manual to accompany Algebra: Form and Function, 2nd Edition.
Algebra: Form and Function, 2nd Edition offers a fresh approach to algebra that focuses on teaching readers how to truly understand the principles, rather than viewing them merely as tools for other forms of mathematics. Meant for a College Algebra course, Algebra: Form and Function, 2nd Edition is an introduction to one of the fundamental aspects of modern society. Algebraic equations describe the laws of science, the principles of engineering, and the rules of business. The power of algebra lies in the efficient symbolic representation of complex ideas, which also presents the main difficulty in learning it. It is easy to forget the underlying structure of algebra and rely instead on a surface knowledge of algebraic manipulations. Most students rely on surface knowledge of algebraic manipulations without understanding the underlying structure of algebra that allows them to see patterns and apply it to multiple situations: McCallum focuses on the structure from the start.
Table of Contents
1 Functions and Algebraic Structure 1
1.1 What is a Function? 2
1.2 Functions and Expressions 8
1.3 Functions and Equations 15
1.4 Functions and Change 24
1.5 Functions, Modeling, and Proportionality 30
Review Problems 36
2 Linear Functions 41
2.1 Introduction to Linear Functions 42
2.2 Linear Expressions 49
2.3 Linear Equations 57
2.4 Equations for Lines in the Plane 65
2.5 Modeling with Linear Functions 73
2.6 Systems of Linear Equations 80
Review Problems 91
Solving Drill 97
3 Quadratic Functions 99
3.1 Introduction to Quadratic Functions 100
3.2 Quadratic Expressions 103
3.3 Converting to Factored and Vertex Form 111
3.4 Quadratic Equations 116
3.5 Factoring Hidden Quadratics 124
3.6 Complex Numbers 129
Review Problems 134
Solving Drill 138
4 Power Functions 139
4.1 Power Functions: Positive Exponents 140
4.2 Power Functions: Negative and Fractional Exponents 146
4.3 Power Functions and Expressions 152
4.4 Power Functions and Equations 158
4.5 Modeling with Power Functions 165
Review Problems 172
Solving Drill 175
5 More On Functions 177
5.1 Domain and Range 178
5.2 Composing and Decomposing Functions 186
5.3 Shifting and Scaling 191
5.4 Inverse Functions 201
Review Problems 206
6 Exponential Functions 209
6.1 Exponential Functions 210
6.2 Exponential Expressions: Growth Rates 216
6.3 Exponential Expressions: Half-Life and Doubling Time 222
6.4 Equations and Exponential Functions 230
6.5 Modeling with Exponential Functions 237
6.6 Exponential Functions and Base e 243
Review Problems 248
7 Logarithms 253
7.1 Introduction to Logarithms 254
7.2 Solving Equations Using Logarithms 263
7.3 Applications of Logarithms to Modeling 269
7.4 Natural Logarithms and Other Bases 274
Review Problems 283
8 Polynomial Functions 287
8.1 Polynomial Functions 288
8.2 Expressions and Polynomial Functions 292
8.3 Solving Polynomial Equations 299
8.4 Long-Run Behavior of Polynomial Functions 306
Review Problems 314
9 Rational Functions 319
9.1 Rational Functions 320
9.2 Long-Run Behavior of Rational Functions 326
9.3 Putting a Rational Function in Quotient Form 337
Review Problems 343
Appendix A: Expressions 345
A.1 Reordering and Regrouping 346
A.2 The Distributive Law 349
Appendix B: Equations 355
B.1 Using the Operations of Arithmetic to Solve Equations 356
Appendix C: Inequalities 361
C.1 Solving Inequalities 362
Appendix D: Quadratics 367
D.1 Quadratic Expressions 368
D.2 Solving Quadratic Equations 375
Appendix E: Algebraic Fractions 377
E.1 Algebraic Fractions 378
E.2 Equations Involving Algebraic Fractions 385
Appendix F: Absolute Value 387
F.1 Absolute Value 388
F.2 Absolute Value Equations and Inequalities 390
Appendix G: Exponents 395
G.1 Exponents with Integer Powers 396
G.2 Exponents with Fractional Powers 405
10 Summation Notation (Online Only) 10-1
10.1 Using Subscripts and Sigma Notation 10-2
11 Sequences and Series (Online Only) 11-1
11.1 Sequences 11-2
11.2 Arithmetic Series 11-8
11.3 Geometric Sequences and Series 11-13
11.4 Applications of Series 11-19
Review Problems 11-25
12 Matrices and Vectors (Online Only) 12-1
12.1 Matrices 12-2
12.2 Matrix Multiplication 12-5
12.3 Matrices and Vectors 12-10
12.4 Matrices and Systems of Linear Equations 12-18
Review Problems 12-28
13 Probability and Statistics (Online Only) 13-1
13.1 The Mean 13-2
13.2 The Standard Deviation 13-9
13.3 Probability 13-14
Review Problems 13-26
Answers to Odd-Numbered Problems 413
Index 431
