Algebra and Trigonometry

Zusammenfassung

Beecher, Penna, and Bittinger’s Algebra and Trigonometry is known for enabling students to “see the math” through its focus on visualization and early introduction to functions. With the Fourth Edition, the authors continue to innovate by incorporating more ongoing review to help students develop their understanding and study effectively.

Mid-chapter Mixed Review exercise sets have been added to give students practice in synthesizing the concepts, and new Study Guide summaries provide built-in tools to help them prepare for tests. MyMathLab has been expanded so that the online content is even more integrated with the text’s approach, with the addition of Vocabulary, Synthesis, and Mid-chapter Mixed Review exercises from the text, as well as example-based videos created by the authors.

Inhalt

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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11. Sequences, Series, and Combinatorics

11.1 Sequences and Series

11.2 Arithmetic Sequences and Series

11.3 geometric Sequences and Series

Visualizing the Graph

11.4 Mathematical Induction

Mid-Chapter Mixed Review

11.5 Combinatorics: Permutations

11.6 Combinatorics: Combinations

11.7 The Binomial Theorem

11.8 Probability

Study Guide

Review Exercises

Chapter Test

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Photo Credits

Answers

Index

Index of Applications