Graphical Approach to Precalculus with Limits, A, 7th edition
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Overview
A Graphical Approach to Precalculus with Limits covers functions through a consistent, 4part 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.
Published by Pearson (December 11th 2020)  Copyright © 2019
ISBN13: 9780137399956
Subject: Precalculus, College Algebra & Trigonometry
Category: Precalculus
Overview
 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
 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 PiecewiseDefined Functions
 2.6 Operations and Composition
 Reviewing Basic Concepts (Sections 2.4  2.6)
 Summary
 Review Exercises
 Test
 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
 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
 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
 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
 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
 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–  .4)
 Summary
 Review Exercises
 Test
 The Unit Circle and the Functions of Trigonometry
 9.1 Angles, Arcs, and Their Measures
 9.2 The Unit Circle and Its Functions
 9.3 Graphs of the Sine and Cosine Functions
 9.4 Graphs of the Other Circular Functions
 9.5 Functions of Angles and Fundamental Angles
 9.6 Evaluating Trigonometric Functions
 9.7 Applications of Right Triangles
 9.8 Harmonic Motion
 Summary
 Review Exercises
 Test
 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
 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
 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
 Limits, Derivatives, and Definite Integrals
 13.1 An Introduction to Limits
 13.2 Techniques for Calculating Limits
 13.3 OneSided Limits and Limits Involving Infinity
 13.4 Tangent Lines and Derivatives
 13.5 Area and the Definite Integral
 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
 Instructor’s Answers
 Answers to Selected Exercises (Note: In the AIE, Instructor’s Answers replaces Answers to Selected Exercises.)
 Index
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