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Summary

This is a new edition of the precalculus text developed by the Consortium based at Harvard University and funded by a National Science Foundation Grant. The text is thought-provoking for well-prepared students while still accessible to students with weaker backgrounds. It provides numerical and graphical approaches as well as algebraic approaches to give students another way of mastering the material. This approach encourages students to persist, thereby lowering failure rates. A large number of real-world examples and problems enable students to create mathematical models that will help them understand the world in which they live. The focus is on those topics that are essential to the study of calculus and these topics are treated in depth. Linear, exponential, power, and periodic functions are introduced before polynomial and rational functions to take advantage of their use to model physical phenomena. Building on the Consortium's Rule of Four: Each function is represented symbolically, numerically, graphically, and verbally where appropriate.

Table of Contents

Functions, Lines, and Change
1(59)
Functions and Function Notation
2(8)
Rate of Change
10(6)
Linear Functions
16(9)
Formulas for Linear Functions
25(8)
Geometric Properties of Linear Functions
33(9)
Fitting Linear Functions to Data
42(17)
Review Problems
48(4)
Check Your Understanding
52(2)
Tools for Chapter One: Linear Equations
54(5)
Functions, Quadratics, and Concavity
59(42)
Input and Output
60(6)
Domain and Range
66(5)
Piecewise Defined Functions
71(6)
Inverse Functions
77(3)
Concavity
80(5)
Quadratic Functions
85(16)
Review Problems
90(3)
Check Your Understanding
93(1)
Tools for Chapter 2: Quadratic Equations
94(7)
Exponential Functions
101(42)
Introduction to the Family of Exponential Functions
102(8)
Comparing Exponential and Linear Functions
110(8)
Graphs of Exponential Functions
118(7)
Continuous Growth and the Number e
125(18)
Review Problems
132(5)
Check Your Understanding
137(2)
Tools for Chapter 3: Exponents
139(4)
Logarithmic Functions
143(38)
Logarithms and their Properties
144(7)
Logarithms and Exponential Models
151(8)
The Logarithmic Function
159(7)
Logarithmic Scales
166(15)
Review Problems
176(3)
Check Your Understanding
179(2)
Transformations of Functions and their Graphs
181(50)
Vertical and Horizontal Shifts
182(9)
Reflections and Symmetry
191(8)
Vertical Stretches and Compressions
199(8)
Horizontal Stretches and Compressions
207(6)
The Family of Quadratic Functions
213(18)
Review Problems
221(4)
Check your Understanding
225(2)
Tools for Chapter 5: Completing the Square
227(4)
Trigonometric Functions
231(64)
Introduction to Periodic Functions
232(6)
The Sine and Cosine Functions
238(8)
Radians
246(6)
Graphs of the Sine and Cosine
252(6)
Sinusoidal Functions
258(9)
Other Trigonometric Functions
267(6)
Inverse Trigonometric Functions
273(22)
Review Problems
282(3)
Check your Understanding
285(3)
Tools for Chapter 6: Right Triangles
288(7)
Trigonometry
295(46)
General Triangles: Laws of Sines and Cosines
296(6)
Trigonometric Identities
302(7)
Sum and Difference Formulas for Sine and Cosine
309(7)
Trigonometric Models
316(9)
Polar Coordinates
325(5)
Complex Numbers and Polar Coordinates
330(11)
Review Problems
337(2)
Check Your Understanding
339(2)
Compositions, Inverses, and Combinations of Functions
341(34)
Composition of Functions
342(8)
Inverse Functions
350(11)
Combinations of Functions
361(14)
Review Problems
370(3)
Check Your Understanding
373(2)
Polynomial and Rational Functions
375(60)
Power Functions
376(8)
Polynomial Functions
384(5)
The Short-run Behavior of Polynomials
389(7)
Rational Functions
396(6)
The Short-run Behavior of Rational Functions
402(8)
Comparing Power, Exponential, and Log Functions
410(6)
Fitting Exponentials and Polynomials to Data
416(19)
Review Problems
423(5)
Check Your Understanding
428(2)
Tools for Chapter 9: Algebraic Fractions
430(5)
Vectors and Matrices
435(40)
Vectors
436(8)
The Components of a Vector
444(5)
Application of Vectors
449(7)
The DOT Product
456(6)
Matrices
462(13)
Review Problems
471(3)
Check Your Understanding
474(1)
Sequences and Series
475(28)
Sequences
476(5)
Defining Functions Using Sums: Arithmetic Series
481(7)
Finite Geometric Series
488(5)
Infinite Geometric Series
493(10)
Review Problems
499(2)
Check Your Understanding
501(2)
Parametric Equations and Conic Sections
503(30)
Parametric Equations
504(10)
Implicitly Defined Curves and Circles
514(4)
Ellipses
518(4)
Hyperbolas
522(4)
Hyperbolic Functions
526(7)
Review Problems
530(1)
Check Your Understanding
531(2)
Answers to Odd-Numbered Problems 533(28)
Index 561

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