Algebra and Trigonometry

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