Precalculus Functions and Graphs A Graphing Approach

by Larson, Ron; Hostetler, Robert P.; Edwards, Bruce H.

• ISBN13: 9780618851508
• ISBN10: 061885150X
• Edition: 5th
• Format: Hardcover
• Copyright: 2007-03-09
• Publisher: Cengage High School

Summary

Part of the market-leadingGraphing Approach Seriesby 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 introducesPrerequisite Skills Review.For selected examples throughout the text, thePrerequisite Skills Reviewdirects 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. New!TheNutshell Appendixreviews the essentials of each function, discussed in theLibrary of Functionsfeature, and offers study capsules with properties, methods, and examples of the major concepts covered in the textbook. This appendix is an ideal study aid for students. New!Progressive Summariesoutline newly introduced topics every three chapters and contextualize them within the framework of the course. New!Make a Decisionexercises--extended modeling applications presented at the end of selected exercise sets--give students the opportunity to apply the mathematical concepts and techniques they've learned to large sets of real data. Updated!The Library of Functions, threaded throughout the text, defines each elementary function and its characteristics at first point of use. The Fifth Edition incorporates new exercises that tests students' understanding of these functions. All elementary functions are also presented in a summary on the front endpapers of the text for convenient reference. Updated!TheChapter Summarieshave been updated to include the Key Terms and Key concepts that are covered in the chapter. These chapter summaries are an effective study aid because they provide a single point of reference for review. Updated!TheProofs of Selected Theoremsare now presented at the end of each chapter for easy reference. The Larson team provides an abundance of features that help students use technology to visualize and understand mathematical concepts.Technology Tipspoint out the pros and cons of technology use in certain mathematical situations. They also provide alternative methods of solving or checking a problem using a graphing calculator. Students may sometimes be misled by the visuals generated by graphing calculators, so the authors use color to enhance the graphing calculator displays in the textbook, where appropriate. This enables students to visualize concepts accurately and efficiently.Technology Supportnotes appear throughout the text and refer students to theTechnology Support Appendix,where they can learn how to use specific graphing calculator features to enhance their understanding of the concepts presented. TheTechnology Supportnotes also direct students to theGraphing Technology Guide,on the textbook's website, for keystroke support for numerous calculator models. Carefully positioned throughout the text,Explorationsengage students in active discovery of mathematical concepts, strengthening critical thinking skills and helping them to develop an intuitive understanding of theoretical concepts. What

Table of Contents

Functions and Their Graphs Introduction to Library of Parent Functions

Lines in the Plane

Functions

Graphs of Functions

Shifting, Reflection, and Stretching Graphs

Combinations of Functions

Inverse Functions

Linear Models and Scatter Plots

Polynomial and Rational Functions

Quadratic Functions

Polynomial Functions of Higher Degree

Real Zeros of Polynomial Functions

Complex Numbers

The Fundamental Theorem of Algebra

Rational Functions and Asymptotes

Graphs of Rational Functions

Quadratic Models Progressive Summary: Chapters 1-2

Exponential and Logarithmic Functions

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Solving Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Nonlinear Models Cumulative Review: Chapters 1-3 Progressive Summary: Chapters 1-3

Trigonometric Functions

Radian and Degree Measure

Trigonometric Functions: The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Analytic Trigonometry

Using Fundamental Identities

Verifying Trigonometric Identities

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple-Angle and Product-to-Sum Formulas

Additional Topics in Trigonometry

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number Cumulative Test: Chapters 4-6 Progressive Summary: Chapters 1-6

Linear Systems and Matrices

Solving Systems of Equations

Systems of Linear Equations in Two Variables

Multivariable Linear Systems

Matrices and Systems of Equations

Operations with Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences, Series, and Probability

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Topics in Analytic Geometry

Circles and Parabolas

Ellipses

Hyperbolas

Rotation and Systems of Quadratic Equations

Parametric Equations

Polar Coordinates

Graphs of Polar Equations

Polar Equations of Conics Cumulative Test: Chapters 7-9 Progressive Summary: Chapters 3-9

Analytic Geometry in Three Dimensions

The Three-Dimensional Coordinate System

Vectors in Space

The Cross Product of Two Vectors

Lines and Planes in Space

Limits and an Introduction to Calculus

Introduction to Limits

Techniques for Evaluating Limits

The Tangent Line Problem

Limits at Infinity and Limits of Sequences

The Area Problem Cumulative Test: Chapters 10-11 Progressive Summary: Chapters 3-11

Technology Support Guide

Review of Graphs, Equations, and Inequalities

The Cartesian Plane

Graphs of Equations

Solving Equations Algebraically and Graphically

Solving Inequalities Algebraically and Graphically

Solving Inequalities Algebraically and Graphically

Representing Data Graphically

Concepts in Statistics

Measures of Central Tendency and Dispersion

Least Squares Regression

Variation

Solving Linear Equations and Inequalities

Systems of Inequalities

Solving Systems of Inequalities

Linear Programming

Study Capsules

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