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Full Description
A Graphical Approach to Precalculus with Limits: A Unit Circle Approach illustrates how the graph of a function can be used to support the solutions of equations and inequalities involving the function. Beginning with linear functions in Chapter 1, the text uses a four-part process to analyze each type of function, starting first with the graph of the function, then the equation, the associated inequality of that equation, and ending with applications. The text covers all of the topics typically caught in a college algebra course, but with an organization that fosters students' understanding of the interrelationships among graphs, equations, and inequalities. With the Fifth Edition, the text continues to evolve as it addresses the changing needs of today's students. Included are additional components to build skills, address critical thinking, solve applications, and apply technology to support traditional algebraic solutions, while maintaining its unique table of contents and functions-based approach. A Graphical Approach to Precalculus with Limits: A Unit Circle Approach continues to incorporate an open design, with helpful features and careful explanations of topics.
Contents
Chapter 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
1.3 Linear Functions
1.4 Equations of Lines and Linear Models
Reviewing Basic Concepts
1.5 Linear Equations and Inequalities
1.6 Applications of Linear Functions
Reviewing Basic Concepts
Summary
Review Exercises
Test
Chapter 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
2.4 Absolute Value Functions
2.5 Piecewise-Defined Functions
2.6 Operations and Composition
Reviewing Basic Concepts
Summary
Review Exercises
Test
Chapter 3 Polynomial Functions
3.1 Complex Numbers
3.2 Quadratic Functions and Graphs
3.3 Quadratic Equations and Inequalities
Reviewing Basic Concepts
3.4 Further Applications of Quadratic Functions and Models
3.5 Higher-Degree Polynomial Functions and Graphs
Reviewing Basic Concepts
3.6 Topics in the Theory of Polynomial Functions (I)
3.7 Topics in the Theory of Polynomial Functions (II)
3.8 Polynomial Equations and Inequalities; Further Applications and Models
Reviewing Basic Concepts
Summary
Review Exercises
Test
Chapter 4 Rational, Power, and Root Functions
4.1 Rational Functions and Graphs
4.2 More on Rational Functions and Graphs
4.3 Rational Equations, Inequalities, Models, and Applications
Reviewing Basic Concepts
4.4 Functions Defined by Powers and Roots
4.5 Equations, Inequalities, and Applications Involving Root Functions
Reviewing Basic Concepts
Summary
Review Exercises
Test
Chapter 5 Inverse, Exponential, and Logarithmic Functions
5.1 Inverse Functions
5.2 Exponential Functions
5.3 Logarithms and Their Properties
Reviewing Basic Concepts
5.4 Logarithmic Functions
5.5 Exponential and Logarithmic Equations and Inequalities
Reviewing Basic Concepts
5.6 Further Applications and Modeling with Exponential and Logarithmic Functions
Summary
Review Exercises
Test
Chapter 6 Analytic Geometry
6.1 Circles and Parabolas
6.2 Ellipses and Hyperbolas
Reviewing Basic Concepts
6.3 Summary of Conic Sections
6.4 Parametric Equations
Reviewing Basic Concepts
Summary
Review Exercises
Test
Chapter 7 Systems of Equations and Inequalities; 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
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
7.7 Systems of Inequalities and Linear Programming
7.8 Partial Fractions
Reviewing Basic Concepts
Summary
Review Exercises
Test
Chapter 8 The Unit Circle and the Functions of Trigonometry
8.1 Angle
