Graphical Approach to Algebra & Trigonometry, A, 7th edition

Margaret L. Lial
, John Hornsby
, Gary K. Rockswold

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A Graphical Approach to Algebra & Trigonometry covers functions through a consistent, 4-part process. The authors ask you to 1: [See] Examine the nature of the graph; 2: Solve a typical equation analytically and graphically; 3: Solve the related inequality analytically and graphically; 4: Apply analytic and graphical methods to solve an application. This proven approach fosters a deep visual and graphical understanding of math, solidifying a stronger connection to the mathematical world around us. Careful chapter layouts, exercises, review questions and chapter features give you a comprehensive roadmap for success in the course. The 7th Edition adds a new Unifying the Function feature after introducing each major class of functions; updates data throughout with new topics including active Twitter users, organic food sales and more; adds nearly 500 new or updated exercises; and much more.

ISBN-13: 9780137399925

Subject: Precalculus, College Algebra & Trigonometry

Category: Algebra & Trigonometry

1. Linear Functions, Equations, and Inequalities

1.1 Real Numbers and the Rectangular Coordinate System
1.2 Introduction to Relations and Functions
Reviewing Basic Concepts (Sections 1.1 - 1.2)
1.3 Linear Functions
1.4 Equations of Lines and Linear Models
Reviewing Basic Concepts (Sections 1.3 - 1.4)
1.5 Linear Equations and Inequalities
Unifying Linear Functions
1.6 Applications of Linear Functions
Reviewing Basic Concepts (Sections 1.5 - 1.6)
Summary
Review Exercises
Test

2. Analysis of Graphs of Functions

2.1 Graphs of Basic Functions and Relations; Symmetry
2.2 Vertical and Horizontal Shifts of Graphs
2.3 Stretching, Shrinking, and Reflecting Graphs
Reviewing Basic Concepts (Sections 2.1 - 2.3)
2.4 Absolute Value Functions
Unifying Absolute Value Functions
2.5 Piecewise-Defined Functions
2.6 Operations and Composition
Reviewing Basic Concepts (Sections 2.4 - 2.6)
Summary
Review Exercises
Test

3. Quadratic Functions

3.1 Complex Numbers
3.2 Quadratic Functions and Graphs
Reviewing Basic Concepts (Sections 3.1 - 3.2)
3.3 Quadratic Equations and Inequalities
Unifying Quadratic Functions
3.4 Applications of Quadratic Functions and Models
Reviewing Basic Concepts (Sections 3.3 - 3.4)
Summary
Review Exercises
Test

4. Polynomial Functions of Higher Degree

4.1 Graphs of Polynomial Functions
4.2 Topics in the Theory of Polynomial Functions (I)
Reviewing Basic Concepts (Sections 4.1 - 4.2)
4.3 Topics in the Theory of Polynomial Functions (II)
4.4 Polynomial Equations, Inequalities, Applications, and Models
Reviewing Basic Concepts (Sections 4.3 - 4.4)
Unifying Polynomial Functions
Summary
Review Exercises
Test

5. Rational, Power, and Root Functions

5.1 Rational Functions and Graphs (I)
5.2 Rational Functions and Graphs (II)
5.3 Rational Equations, Inequalities, Models, and Applications
Reviewing Basic Concepts (Sections 5.1 - 5.3)
5.4 Functions Defined by Powers and Roots
5.5 Equations, Inequalities, and Applications Involving Root Functions
Reviewing Basic Concepts (Sections 5.4 - 5.5)
Unifying Root Functions
Summary
Review Exercises
Test

6. Inverse, Exponential, and Logarithmic Functions

6.1 Inverse Functions
6.2 Exponential Functions
Unifying Exponential Functions
6.3 Logarithms and Their Properties
Reviewing Basic Concepts (Sections 6.1 - 6.3)
6.4 Logarithmic Functions
6.5 Exponential and Logarithmic Equations and Inequalities
Unifying Logarithmic Functions
6.6 Further Applications and Modeling with Exponential and Logarithmic Functions
Reviewing Basic Concepts (Sections 6.4 - 6.6)
Summary Exercises on Functions: Domains, Defining Equations, and Composition
Summary
Review Exercises
Test

7. Systems and Matrices

7.1 Systems of Equations
7.2 Solution of Linear Systems in Three Variables
7.3 Solution of Linear Systems by Row Transformations
Reviewing Basic Concepts (Sections 7.1 - 7.3)
7.4 Matrix Properties and Operations
7.5 Determinants and Cramer's Rule
7.6 Solution of Linear Systems by Matrix Inverses
Reviewing Basic Concepts (Sections 7.4 - 7.6)
7.7 Systems of Inequalities and Linear Programming
7.8 Partial Fractions
Reviewing Basic Concepts (Sections 7.7 - 7.8)
Summary
Review Exercises
Test

8. Conic Sections, Nonlinear Systems, and Parametric Equations

8.1 Circles Revisited and Parabolas
8.2 Ellipses and Hyperbolas
Reviewing Basic Concepts (Sections 8.1 - 8.2)
8.3 The Conic Sections and Nonlinear Systems
8.4 Introduction to Parametric Equations
Reviewing Basic Concepts (Sections 8.3 - 8.4)
Summary
Review Exercises
Test

9. Trigonometric Functions and Applications

9.1 Angles, Arcs, and Their Measures
9.2 Trigonometric Functions and Fundamental Identities
9.3 Right Triangles and Evaluating Trigonometric Functions
9.4 Applications of Right Triangles
9.5 The Circular Functions
9.6 Graphs of the Sine and Cosine Functions
9.7 Graphs of the Other Circular Functions
9.8 Harmonic Motion
Summary
Review Exercises
Test

10. Trigonometric Identities and Equations

10.1 Trigonometric Identities
10.2 Sum and Difference Identities
10.3 Further Identities
10.4 The Inverse Circular Functions
10.5 Trigonometric Equations and Inequalities (I)
10.6 Trigonometric Equations and Inequalities (II)
Unifying Trigonometric Functions
Summary
Review Exercises
Test

11. Applications of Trigonometry and Vectors

11.1 The Law of Sines
11.2 The Law of Cosines and Area Formulas
11.3 Vectors and Their Applications
11.4 Trigonometric (Polar) Form of Complex Numbers
11.5 Powers and Roots of Complex Numbers
11.6 Polar Equations and Graphs
11.7 More Parametric Equations
Summary
Review Exercises
Test

12. Further Topics in Algebra

12.1 Sequences and Series
12.2 Arithmetic Sequences and Series
12.3 Geometric Sequences and Series
Reviewing Basic Concepts (Sections 12.1 - 12.3)
12.4 Counting Theory
12.5 The Binomial Theorem
Reviewing Basic Concepts (Sections 12.4 -12.5)
12.6 Mathematical Induction
12.7 Probability
Reviewing Basic Concepts (Sections 12.6 - 12.7)
Summary
Review Exercises
Test

R. Review: Basic Algebraic Concepts

R.1 Review of Sets
R.2 Review of Exponents and Polynomials
R.3 Review of Factoring
R.4 Review of Rational Expressions
R.5 Review of Negative and Rational Exponents
R.6 Review of Radicals
Test

Appendices

A: Geometry Formulas
B: Vectors in Space
C: Polar Form of Conic Sections
D: Rotation of Axes