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College Algebra

A complete precalculus toolkit: equations and inequalities, polynomial, rational, exponential, and logarithmic functions, trigonometry, systems, analytic geometry, and a first look at limits. These exercises build the function fluency and algebraic stamina calculus demands.

Merged from College Algebra 2e, Algebra and Trigonometry 2e, Precalculus 2e & College Algebra with Corequisite Support 2e

4,390 exercises90 sections

Status

Sections

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Prerequisites

356

1.1 Real Numbers: Algebra Essentials58

1.2 Exponents and Scientific Notation56

1.3 Radicals and Rational Exponents63

1.4 Polynomials44

1.5 Factoring Polynomials46

1.6 Rational Expressions89

Equations and Inequalities

338

2.1 The Rectangular Coordinate Systems and Graphs29

2.2 Linear Equations in One Variable53

2.3 Models and Applications37

2.4 Complex Numbers41

2.5 Quadratic Equations47

2.6 Other Types of Equations45

2.7 Linear Inequalities and Absolute Value Inequalities86

Functions

333

3.1 Functions and Function Notation50

3.2 Domain and Range35

3.3 Rates of Change and Behavior of Graphs28

3.4 Composition of Functions66

3.5 Transformation of Functions38

3.6 Absolute Value Functions38

3.7 Inverse Functions78

Linear Functions

322

4.1 Linear Functions114

4.2 Modeling with Linear Functions66

4.3 Fitting Linear Models to Data104

2.2 Graphs of Linear Functions38

Polynomial and Rational Functions

455

5.1 Quadratic Functions70

5.2 Power Functions and Polynomial Functions38

5.3 Graphs of Polynomial Functions39

5.4 Dividing Polynomials38

5.5 Zeros of Polynomial Functions51

5.6 Rational Functions41

5.7 Inverses and Radical Functions55

5.8 Modeling Using Variation83

3.1 Complex Numbers40

Exponential and Logarithmic Functions

388

6.1 Exponential Functions55

6.2 Graphs of Exponential Functions24

6.3 Logarithmic Functions53

6.4 Graphs of Logarithmic Functions30

6.5 Logarithmic Properties53

6.6 Exponential and Logarithmic Equations61

6.7 Exponential and Logarithmic Models40

6.8 Fitting Exponential Models to Data72

The Unit Circle: Sine and Cosine Functions

204

7.2 Right Triangle Trigonometry27

7.3 Unit Circle51

7.4 The Other Trigonometric Functions83

Periodic Functions

96

8.1 Graphs of the Sine and Cosine Functions20

8.2 Graphs of the Other Trigonometric Functions10

8.3 Inverse Trigonometric Functions66

Trigonometric Identities and Equations

319

9.1 Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions35

9.2 Sum and Difference Identities37

9.3 Double-Angle, Half-Angle, and Reduction Formulas43

9.4 Sum-to-Product and Product-to-Sum Formulas44

9.5 Solving Trigonometric Equations117

7.6 Modeling with Trigonometric Functions43

Further Applications of Trigonometry

260

10.1 Non-right Triangles: Law of Sines25

10.2 Non-right Triangles: Law of Cosines25

10.3 Polar Coordinates30

10.4 Polar Coordinates: Graphs21

10.5 Polar Form of Complex Numbers40

10.6 Parametric Equations34

10.7 Parametric Equations: Graphs12

Systems of Equations and Inequalities

396

11.1 Systems of Linear Equations: Two Variables55

11.2 Systems of Linear Equations: Three Variables43

11.3 Systems of Nonlinear Equations and Inequalities: Two Variables27

11.4 Partial Fractions41

11.5 Matrices and Matrix Operations43

11.6 Solving Systems with Gaussian Elimination48

11.7 Solving Systems with Inverses44

11.8 Solving Systems with Cramer's Rule95

Analytic Geometry

165

12.1 The Ellipse33

12.2 The Hyperbola26

12.3 The Parabola28

12.4 Rotation of Axes23

12.5 Conic Sections in Polar Coordinates55

Sequences, Probability, and Counting Theory

352

13.1 Sequences and Their Notations45

13.2 Arithmetic Sequences50

13.3 Geometric Sequences43

13.4 Series and Their Notations55

13.5 Counting Principles43

13.6 Binomial Theorem29

13.7 Probability87

Trigonometric Functions

204

5.2 Unit Circle: Sine and Cosine Functions51

5.3 The Other Trigonometric Functions51

5.4 Right Triangle Trigonometry59

Introduction to Calculus

202

12.1 Finding Limits: Numerical and Graphical Approaches30

12.2 Finding Limits: Properties of Limits46

12.3 Continuity34

12.4 Derivatives92

Adapted from College Algebra © 2021 Rice University. Licensed under CC BY 4.0. Sources: College Algebra 2e, Algebra and Trigonometry 2e, Precalculus 2e, College Algebra with Corequisite Support 2e. Imported at revision 4922e46.