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Table of Contents

1 The Key Concepts of Algebra

1.1 EXPRESSIONS
1.2 EQUATIONS
1.3 EQUIVALENT EXPRESSIONS
1.4 EQUIVALENT EQUATIONS
REVIEW PROBLEMS

2 Rules for Expressions and the Reasons for Them

2.1 REORDERING AND REGROUPING
2.2 THE DISTRIBUTIVE LAW
2.3 EXPANDING AND FACTORING
2.4 ALGEBRAIC FRACTIONS
REVIEW PROBLEMS

3 Rules for Equations and the Reasons for Them

3.1 SOLVING EQUATIONS
3.2 SOLVING INEQUALITIES
3.3 ABSOLUTE VALUE EQUATIONS AND INEQUALITIES
REVIEW PROBLEMS

4 Functions, Expressions, and Equations

4.1 WHAT IS A FUNCTION?
4.2 FUNCTIONS AND EXPRESSIONS
4.3 FUNCTIONS AND EQUATIONS
4.4 FUNCTIONS AND CHANGE
4.5 FUNCTIONS AND MODELING
REVIEW PROBLEMS

5 Linear Functions, Expressions, and Equations

5.1 LINEAR FUNCTIONS
5.2 WORKING WITH LINEAR EXPRESSIONS
5.3 SOLVING LINEAR EQUATIONS
5.4 EQUATIONS FOR LINES IN THE PLANE
5.5 MODELING WITH LINEAR FUNCTIONS AND EQUATIONS
5.6 SYSTEMS OF LINEAR EQUATIONS
REVIEW PROBLEMS
FOCUS ON PRACTICE

6 Rules for Exponents and the Reasons for Them

6.1 INTEGER POWERS AND THE EXPONENT RULES
6.2 FRACTIONAL EXPONENTS AND RADICAL EXPRESSIONS
REVIEW PROBLEMS

7 Power Functions, Expressions, and Equations

7.1 POWER FUNCTIONS
7.2 WORKING WITH POWER EXPRESSIONS
7.3 SOLVING POWER EQUATIONS
7.4 MODELING WITH POWER FUNCTIONS
REVIEW PROBLEMS
FOCUS ON PRACTICE

8 More on Functions

8.1 DOMAIN AND RANGE
8.2 COMPOSING AND DECOMPOSING FUNCTIONS
8.3 SHIFTING AND SCALING
8.4 INVERSE FUNCTIONS
REVIEW PROBLEMS

9 Quadratic Functions, Expressions, and Equations

9.1 QUADRATIC FUNCTIONS
9.2 WORKING WITH QUADRATIC EXPRESSIONS
9.3 SOLVING QUADRATIC EQUATIONS BY COMPLETING THE SQUARE
9.4 SOLVING QUADRATIC EQUATIONS BY FACTORING
9.5 COMPLEX NUMBERS
REVIEW PROBLEMS
FOCUS ON PRACTICE

10 Exponential Functions, Expressions, and Equations

10.1 EXPONENTIAL FUNCTIONS
10.2 WORKING WITH THE BASE
10.3 WORKING WITH THE EXPONENT
10.4 SOLVING EXPONENTIAL EQUATIONS
10.5 MODELING WITH EXPONENTIAL FUNCTIONS
10.6 EXPONENTIAL FUNCTIONS AND BASE e
REVIEW PROBLEMS

11 Logarithms

11.1 INTRODUCTION TO LOGARITHMS
11.2 SOLVING EQUATIONS USING LOGARITHMS
11.3 APPLICATIONS OF LOGARITHMS TO MODELING
11.4 NATURAL LOGARITHMS AND OTHER BASES
REVIEW PROBLEMS

12 Polynomials

12.1 POLYNOMIAL FUNCTIONS
12.2 WORKING WITH POLYNOMIALS
12.3 SOLVING POLYNOMIAL EQUATIONS
12.4 LONG-RUN BEHAVIOR OF POLYNOMIAL FUNCTIONS
REVIEW PROBLEMS

13 Rational Functions

13.1 RATIONAL FUNCTIONS
13.2 LONG-RUN BEHAVIOR OF RATIONAL FUNCTIONS
13.3 PUTTING A RATIONAL FUNCTION IN QUOTIENT FORM
REVIEW PROBLEMS

14 Summation Notation

14.1 USING SUBSCRIPTS AND SIGMA NOTATION

15 Sequences and Series

15.1 SEQUENCES
15.2 ARITHMETIC SERIES
15.3 GEOMETRIC SEQUENCES AND SERIES
15.4 APPLICATIONS OF SERIES
REVIEW PROBLEMS

16 Matrices and Vectors

16.1 MATRICES
16.2 MATRIX MULTIPLICATION
16.3 MATRICES AND VECTORS
16.4 MATRICES AND SYSTEMS OF LINEAR EQUATIONS
REVIEW PROBLEMS

17 Probability and Statistics

17.1 THE MEAN
17.2 THE STANDARD DEVIATION
17.3 PROBABILITY
REVIEW PROBLEMS

INDEX