Algebra and Trigonometry

Judy Beecher has an undergraduate degree in mathematics from Indiana University and a graduate degree in mathematics from Purdue University. She has taught at both the high school and college levels with many years of developmental math and precalculus teaching experience at Indiana University–Purdue University Indianapolis (IUPUI). In addition to her career in textbook publishing, she enjoys traveling, spending time with her grandchildren, and promoting charity projects for a children's camp.   Judy Penna received her undergraduate degree in mathematics from Kansas State University and her graduate degree in mathematics from the University of Illinois. Since then, she has taught at Indiana University–Purdue University Indianapolis (IUPUI) and at Butler University, and continues to focus on writing quality textbooks for undergraduate mathematics students. In her free time she likes to travel, read, knit and spend time with her children.   Marvin Bittinger has been teaching math at the university level for more than thirty-eight years. Since 1968, he has been employed at Indiana University–Purdue University Indianapolis (IUPUI), and is now professor emeritus of mathematics education. Professor Bittinger has authored over 190 publications on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy and his election to the Manchester College Board of Trustees from 1992 to 1999. His hobbies include hiking in Utah, baseball, golf, and bowling. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana with his wife Elaine. He has two grown and married sons, Lowell and Chris, and four granddaughters.

R. Basic Concepts of Algebra

R.1 The Real-Number Systemeal Numbers

R.2 Integer Exponents, Scientific Notation, and Order of Operations

R.3 Addition, Subtraction, and Multiplication of Polynomials

R.4 Factoring Terms with Common Factors

R.5 The Basics of Equation Solving

R.6 Rational Expressions

R.7 Radical Notation and Rational Exponents

Study Guide

Review Exercises

Chapter Test

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1. Graphs; Linear Functions and Models

1.1 Introduction to Graphing

Visualizing the Graph

1.2 Functions and Graphs

1.3 Linear Functions, Slope, and Applications

Visualizing the Graph

Mid-Chapter Mixed Review

1.4 Equations of Lines and Modeling

1.5 Linear Equations, Functions, Zeros, and Applications

1.6 Solving Linear Inequalities

Study Guide

Review Exercises

Chapter Test

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2. More on Functions

2.1 Increasing, Decreasing, and Piecewise Functions; Applications

2.2 The Algebra of Functions

2.3 The Composition of Functions

Mid-Chapter Mixed Review

2.4 Symmetry and Transformations

Visualizing the Graph

2.5 Variation and Applications

Study Guide

Review Exercises

Chapter Test

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3. Quadratic Functions and Equations; Inequalities

3.1 The Complex Numbers

3.2 Quadratic Equations, Functions, Zeros, and Models

3.3 Analyzing Graphs of Quadratic Functions

Visualizing the Graph

Mid-Chapter Mixed Review

3.4 Solving Rational Equations and Radical Equations

3.5 Solving Linear Inequalities

Study Guide

Review Exercises

Chapter Test

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4. Polynomial and Rational Functions

4.1 Polynomial Functions and Modeling

4.2 Graphing Polynomial Functions

Visualizing the Graph

4.3 Polynomial Division; The Remainder and Factor Theorems

Mid-Chapter Mixed Review

4.4 Theorems about Zeros of Polynomial Functions

4.5 Rational Functions

Visualizing the Graph

4.6 Polynomial and Rational Inequalities

Study Guide

Review Exercises

Chapter Test

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5. Exponential and Logarithmic Functions

5.1 Inverse Functions

5.2 Exponential Functions and Graphs

5.3 Logarithmic Functions and Graphs

Mid-Chapter Mixed Review

5.4 Properties of Logarithmic Functions

5.5 Solving Exponential Equations and Logarithmic Equations

5.6 Applications and Models: Growth and Decay; Compound Interest

Study Guide

Review Exercises

Chapter Test

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6. The Trigonometric Functions

6.1 Trigonometric Functions of Acute Angles

6.2 Applications of Right Triangles

6.3 Trigonometric Functions of Any Angle

¿ Mid-Chapter Mixed Review

6.4 Radians, Arc Length, and Angular Speed

6.5 Circular Functions: Graphs and Properties

6.6 Graphs of Transformed Sine and Cosine Functions

Visualizing the Graph

Study Guide

Review Exercises

Chapter Test

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7. Trigonometric Identities, Inverse Functions, and Equations

7.1 Identities: Pythagorean and Sum and Difference

7.2 Identities: Cofunction, Double-Angle, and Half-Angle

7.3 Proving Trigonometric Identities

Mid-Chapter Mixed Review

7.4 Inverses of the Trigonometric Functions

7.5 Solving Trigonometric Equations

Visualizing the Graph

Study Guide

Review Exercises

Chapter Test

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8. Applications of Trigonometry

8.1 The Law of Sines

8.2 The Law of Cosines

8.3 Complex Numbers: Trigonometric Form

Mid-Chapter Mixed Review

8.4 Polar Coordinates and Graphs

Visualizing the Graph

8.5 Vectors and Applications

8.6 Vector Operations

Study Guide

Review Exercises

Chapter Test

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9. Systems of Equations and Matrices

9.1 Systems of Equations in Two Variables

Visualizing the Graph

9.2 Systems of Equations in Three Variables

9.3 Matrices and Systems of Equations

9.4 Matrix Operations

9.5 Inverses of Matrices

9.6 Determinants and Cramer’s Rule

9.7 Systems of Inequalities and Linear Programming

9.8 Partial Fractions

Study Guide

Review Exercises

Chapter Test

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10. Analytic Geometry Topics

10.1 The Parabola

10.2 The Circle and the Ellipse

10.3 The Hyperbola

10.4 Nonlinear Systems of Equations and Inequalities

Visualizing the Graph

Mid-Chapter Mixed Review

10.5 Rotation of Axes

10.6 Polar Equations of Conics

10.7 Parametric Equations

Study Guide

Review Exercises

Chapter Test

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Photo Credits

Answers

Index

Index of Applications