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Part of the market-leading Graphing Approach Series by Larson, Hostetler, and Edwards, Precalculus Functions and Graphs: A Graphing Approach, 5/e, is an ideal student and instructor resource for courses that require the use of a graphing calculator. The quality and quantity of the exercises, combined with interesting applications and innovative resources, make teaching easier and help students succeed.
Continuing the series' emphasis on student support, the Fifth Edition introduces Prerequisite Skills Review. For selected examples throughout the text, the Prerequisite Skills Review directs students to previous sections in the text to review concepts and skills needed to master the material at hand. In addition, prerequisite skills review exercises in Eduspace (see below for description) are referenced in every exercise set.
The Larson team achieves accessibility through careful writing and design, including examples with detailed solutions that begin and end on the same page, which maximizes the readability of the text. Similarly, side-by-side solutions show algebraic, graphical, and numerical representations of the mathematics and support a variety of learning styles.
1. Functions and Their Graphs
Introduction to Library of Functions
1.1 Lines in the Plane
1.2 Functions
1.3 Graphs of Functions
1.4 Shifting, Reflection, and Stretching Graphs
1.5 Combinations of Functions
1.6 Inverse Functions
1.7 Linear Models and Scatter Plots
2. Polynomial and Rational Functions
2.1 Quadratic Functions
2.2 Polynomial Functions of Higher Degree
2.3 Real Zeros of Polynomial Functions
2.4 Complex Numbers
2.5 The Fundamental Theorem of Algebra
2.6 Rational Functions and Asymptotes
2.7 Graphs of Rational Functions
2.8 Quadratic Models
Progressive Summary: Chapters 1-2
3. Exponential and Logarithmic Functions
3.1 Exponential Functions and Their Graphs
3.2 Logarithmic Functions and Their Graphs
3.3 Properties of Logarithms
3.4 Solving Exponential and Logarithmic Equations
3.5 Exponential and Logarithmic Models
3.6 Nonlinear Models
Cumulative Review: Chapters 1-3
Progressive Summary: Chapters 1-3
4. Trigonometric Functions
4.1 Radian and Degree Measure
4.2 Trigonometric Functions: The Unit Circle
4.3 Right Triangle Trigonometry
4.4 Trigonometric Functions of Any Angle
4.5 Graphs of Sine and Cosine Functions
4.6 Graphs of Other Trigonometric Functions
4.7 Inverse Trigonometric Functions
4.8 Applications and Models
5. Analytic Trigonometry
5.1 Using Fundamental Identities
5.2 Verifying Trigonometric Identities
5.3 Solving Trigonometric Equations
5.4 Sum and Difference Formulas
5.5 Multiple-Angle and Product-to-Sum Formulas
6. Additional Topics in Trigonometry
6.1 Law of Sines
6.2 Law of Cosines
6.3 Vectors in the Plane
6.4 Vectors and Dot Products
6.5 Trigonometric Form of a Complex Number
Cumulative Test: Chapters 4-6
Progressive Summary: Chapters 1-6
7. Linear Systems and Matrices
7.1 Solving Systems of Equations
7.2 Systems of Linear Equations in Two Variables
7.3 Multivariable Linear Systems
7.4 Matrices and Systems of Equations
7.5 Operations with Matrices
7.6 The Inverse of a Square Matrix
7.7 The Determinant of a Square Matrix
7.8 Applications of Matrices and Determinants
8. Sequences, Series, and Probability
8.1 Sequence and Series
8.2 Arithmetic Sequences and Partial Sums
8.3 Geometric Sequences and Series
8.4 Mathematical Induction
8.5 The Binomial Theorem
8.6 Counting Principals
8.7 Probability
Progressive Summary: Chapters 1-8
9. Topics in Analytic Geometry
9.1 Conics: Circles and Parabolas
9.2 Conics: Ellipses
9.3 Conics: Hyperbolas
9.4 Rotation and Systems of Quadratic Equations
9.5 Parametric Equations
9.6 Polar Coordinates
9.7 Graphs of Polar Equations
9.8 Polar Equations of Conics
Cumulative Test: Chapters 7-9
10. Analytic Geometry in Three Dimensions
10.1 The Three-Dimensional Coordinate System
10.2 Vectors in Space
10.3 The Cross Product of Two Vectors
10.4 Lines and Planes in Space
11. Limits and an Introduction to Calculus
11.1 Introduction to Limits
11.2 Techniques for Evaluating Limits
11.3 The Tangent Line Problem
11.4 Limits at Infinity and Limits of Sequences
11.5 The Area Problem
Cumulative Test: Chapters 10-11
Progressive Summary: Chapters 1-11
Appendix A. Technology Support Guide
Appendix B. Review of Graphs, Equations, and Inequalities
B.1 The Cartesian Plane
B.2 Graphs of Equations
B.3 Solving Quadratic Equations Algebraically and Graphically
B.4 Solving Other Equations Algebraically and Graphically
B.5 Solving Inequalities Algebraically and Graphically
B.6 Representing Data Graphically
Appendix C. Concepts in Statistics
C.1 Measures of Central Tendency and Dispersion
C.2 Least Squares Regression
Appendix D. Variation
D.1 Direct Variation
D.2 Direct Variation as an nth Power
D.3 Inverse Variation
D4 Joint Variation
Appendix E. Solving Linear Equations and Inequalities
Appendix F. Systems of Inequalities
F.1 Solving Systems of Inequalities
F.2 Linear Programming
Appendix G Study Capsules
Ron Larson, Robert P. Hostetler and Bruce H. Edwards
ISBN13: 978-0618851508Part of the market-leading Graphing Approach Series by Larson, Hostetler, and Edwards, Precalculus Functions and Graphs: A Graphing Approach, 5/e, is an ideal student and instructor resource for courses that require the use of a graphing calculator. The quality and quantity of the exercises, combined with interesting applications and innovative resources, make teaching easier and help students succeed.
Continuing the series' emphasis on student support, the Fifth Edition introduces Prerequisite Skills Review. For selected examples throughout the text, the Prerequisite Skills Review directs students to previous sections in the text to review concepts and skills needed to master the material at hand. In addition, prerequisite skills review exercises in Eduspace (see below for description) are referenced in every exercise set.
The Larson team achieves accessibility through careful writing and design, including examples with detailed solutions that begin and end on the same page, which maximizes the readability of the text. Similarly, side-by-side solutions show algebraic, graphical, and numerical representations of the mathematics and support a variety of learning styles.
Table of Contents
1. Functions and Their Graphs
Introduction to Library of Functions
1.1 Lines in the Plane
1.2 Functions
1.3 Graphs of Functions
1.4 Shifting, Reflection, and Stretching Graphs
1.5 Combinations of Functions
1.6 Inverse Functions
1.7 Linear Models and Scatter Plots
2. Polynomial and Rational Functions
2.1 Quadratic Functions
2.2 Polynomial Functions of Higher Degree
2.3 Real Zeros of Polynomial Functions
2.4 Complex Numbers
2.5 The Fundamental Theorem of Algebra
2.6 Rational Functions and Asymptotes
2.7 Graphs of Rational Functions
2.8 Quadratic Models
Progressive Summary: Chapters 1-2
3. Exponential and Logarithmic Functions
3.1 Exponential Functions and Their Graphs
3.2 Logarithmic Functions and Their Graphs
3.3 Properties of Logarithms
3.4 Solving Exponential and Logarithmic Equations
3.5 Exponential and Logarithmic Models
3.6 Nonlinear Models
Cumulative Review: Chapters 1-3
Progressive Summary: Chapters 1-3
4. Trigonometric Functions
4.1 Radian and Degree Measure
4.2 Trigonometric Functions: The Unit Circle
4.3 Right Triangle Trigonometry
4.4 Trigonometric Functions of Any Angle
4.5 Graphs of Sine and Cosine Functions
4.6 Graphs of Other Trigonometric Functions
4.7 Inverse Trigonometric Functions
4.8 Applications and Models
5. Analytic Trigonometry
5.1 Using Fundamental Identities
5.2 Verifying Trigonometric Identities
5.3 Solving Trigonometric Equations
5.4 Sum and Difference Formulas
5.5 Multiple-Angle and Product-to-Sum Formulas
6. Additional Topics in Trigonometry
6.1 Law of Sines
6.2 Law of Cosines
6.3 Vectors in the Plane
6.4 Vectors and Dot Products
6.5 Trigonometric Form of a Complex Number
Cumulative Test: Chapters 4-6
Progressive Summary: Chapters 1-6
7. Linear Systems and Matrices
7.1 Solving Systems of Equations
7.2 Systems of Linear Equations in Two Variables
7.3 Multivariable Linear Systems
7.4 Matrices and Systems of Equations
7.5 Operations with Matrices
7.6 The Inverse of a Square Matrix
7.7 The Determinant of a Square Matrix
7.8 Applications of Matrices and Determinants
8. Sequences, Series, and Probability
8.1 Sequence and Series
8.2 Arithmetic Sequences and Partial Sums
8.3 Geometric Sequences and Series
8.4 Mathematical Induction
8.5 The Binomial Theorem
8.6 Counting Principals
8.7 Probability
Progressive Summary: Chapters 1-8
9. Topics in Analytic Geometry
9.1 Conics: Circles and Parabolas
9.2 Conics: Ellipses
9.3 Conics: Hyperbolas
9.4 Rotation and Systems of Quadratic Equations
9.5 Parametric Equations
9.6 Polar Coordinates
9.7 Graphs of Polar Equations
9.8 Polar Equations of Conics
Cumulative Test: Chapters 7-9
10. Analytic Geometry in Three Dimensions
10.1 The Three-Dimensional Coordinate System
10.2 Vectors in Space
10.3 The Cross Product of Two Vectors
10.4 Lines and Planes in Space
11. Limits and an Introduction to Calculus
11.1 Introduction to Limits
11.2 Techniques for Evaluating Limits
11.3 The Tangent Line Problem
11.4 Limits at Infinity and Limits of Sequences
11.5 The Area Problem
Cumulative Test: Chapters 10-11
Progressive Summary: Chapters 1-11
Appendix A. Technology Support Guide
Appendix B. Review of Graphs, Equations, and Inequalities
B.1 The Cartesian Plane
B.2 Graphs of Equations
B.3 Solving Quadratic Equations Algebraically and Graphically
B.4 Solving Other Equations Algebraically and Graphically
B.5 Solving Inequalities Algebraically and Graphically
B.6 Representing Data Graphically
Appendix C. Concepts in Statistics
C.1 Measures of Central Tendency and Dispersion
C.2 Least Squares Regression
Appendix D. Variation
D.1 Direct Variation
D.2 Direct Variation as an nth Power
D.3 Inverse Variation
D4 Joint Variation
Appendix E. Solving Linear Equations and Inequalities
Appendix F. Systems of Inequalities
F.1 Solving Systems of Inequalities
F.2 Linear Programming
Appendix G Study Capsules