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Fundamentals of Precalculus,9780321122322
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Fundamentals of Precalculus

by
Edition:
1st
ISBN13:

9780321122322

ISBN10:
0321122321
Format:
Hardcover
Pub. Date:
1/1/2004
Publisher(s):
Addison Wesley

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Summary

Fundamentals of Precalculus is designed to review the fundamental topics that are necessary for success in calculus. Containing only five chapters, this text can be covered in a one-semester or one-term course with a minimum of deleting or skipping around. A student who is well acquainted with the material in this text will have the necessary skills, understanding, and insights required in calculus.

Table of Contents

Preface xiii
Supplements xvii
Graphs and Functions
1(105)
Real Numbers and Their Properties
2(9)
The Real Numbers
2(2)
Properties of the Real Numbers
4(1)
Additive Inverses
5(1)
Relations
6(1)
Absolute Value
6(3)
Equations Involving Absolute Value
9(2)
Linear and Absolute Value Inequalities
11(10)
Interval Notation
11(1)
Linear Inequalities
12(2)
Compound Inequalities
14(2)
Absolute Value Inequalities
16(2)
Modeling with Inequalities
18(3)
Equations and Graphs in Two Variables
21(11)
The Cartesian Coordinate System
21(1)
The Distance Formula
22(1)
The Midpoint Formula
23(1)
The Circle
24(3)
The Line
27(2)
Using a Graph to Solve an Equation
29(3)
Linear Equations in Two Variables
32(11)
Slope of a Line
32(2)
Point-Slope Form
34(1)
Slope-Intercept Form
35(1)
Using Slope to Graph a Line
36(1)
The Three Forms for the Equation of a Line
37(1)
Parallel Lines
38(1)
Perpendicular Lines
39(1)
Applications
40(3)
Functions
43(12)
The Function Concept
43(1)
Identifying Functions
44(3)
Domain and Range
47(1)
Function Notation
48(2)
The Average Rate of Change of a Function
50(2)
Constructing Functions
52(3)
Graphs of Relations and Functions
55(12)
Graphing Equations
55(3)
Semicircles
58(1)
Piecewise Functions
59(3)
Increasing, Decreasing, and Constant
62(5)
Families of Functions, Transformations, and Symmetry
67(12)
Translation
67(3)
Reflection
70(2)
Stretching and Shrinking
72(2)
The Linear Family of Functions
74(1)
Symmetry
74(5)
Operations with Functions
79(9)
Basic Operations with Functions
79(3)
Composition of Functions
82(3)
Applications
85(3)
Inverse Functions
88(18)
One-to-One and Invertible Functions
88(1)
Determining Whether a Function Is One-to-One
89(2)
Inverse Functions Using Function Notation
91(2)
Graphs of f and f-1
93(1)
Finding Inverse Functions Mentally
94(5)
Highlights
99(2)
Chapter 1 Review Exercises
101(4)
Concepts of Calculus: Limits
105(1)
Polynomial and Rational Functions
106(74)
Quadratic Functions and Inequalities
107(8)
Two Forms for a Quadratic Function
107(2)
Opening, Vertex, and Axis of Symmetry
109(1)
Intercepts
110(1)
Quadratic Inequalities
111(2)
Applications of Maximum and Minimum
113(2)
Complex Numbers
115(7)
Definitions
115(2)
Addition, Subtraction, and Multiplication
117(1)
Division of Complex Numbers
118(1)
Roots of Negative Numbers
119(1)
Imaginary Solutions to Quadratic Equations
120(2)
Zeros of Polynomial Functions
122(11)
The Remainder Theorem
122(1)
Synthetic Division
123(3)
The Factor Theorem
126(1)
The Fundamental Theorem of Algebra
127(1)
The Rational Zero Theorem
127(6)
The Theory of Equations
133(6)
The Number of Roots of a Polynomial Equation
133(1)
The Conjugate Pairs Theorem
134(1)
Descartes' Rule of Signs
135(4)
Miscellaneous Equations
139(10)
Factoring Higher-Degree Equations
139(1)
Equations Involving Square Roots
140(2)
Equations with Rational Exponents
142(1)
Equations of Quadratic Type
143(2)
Equations Involving Absolute Value
145(4)
Graphs of Polynomial Functions
149(11)
Drawing Good Graphs
149(1)
Symmetry
149(2)
Behavior at the x-Intercepts
151(1)
The Leading Coefficient Test
151(3)
Sketching Graphs of Polynomial Functions
154(1)
Polynomial Inequalities
155(5)
Rational Functions and Inequalities
160(20)
Rational Functions and Their Domains
160(1)
Horizontal and Vertical Asymptotes
161(2)
Oblique Asymptotes
163(1)
Sketching Graphs of Rational Functions
164(4)
Rational Inequalities
168(1)
Applications
169(5)
Highlights
174(1)
Chapter 2 Review Exercises
175(4)
Concepts of Calculus: Instantaneous rate of change
179(1)
Trigonometric Functions
180(104)
Angles and Their Measurements
181(10)
Degree Measure of Angles
181(4)
Radian Measure of Angles
185(3)
Arc Length
188(3)
The Sine and Cosine Functions
191(8)
Definition
191(2)
Sine and Cosine of a Multiple of a 45°
193(1)
Sine and Cosine of a Multiple of a 30°
194(1)
Sine and Cosine of an Arc
195(1)
Approximate Values for Sine and Cosine
196(1)
The Fundamental Identity
196(1)
Modeling the Motion of a Spring
197(2)
The Graphs of the Sine and Cosine Functions
199(14)
The Graph of y = sin(x)
199(3)
The Graph of y = cos(x)
202(1)
Transformations of Sine and Cosine
203(2)
Changing the Period
205(2)
The General Sine Wave
207(2)
Frequency
209(4)
The Other Trigonometric Functions and Their Graphs
213(11)
Definitions
213(2)
Graph of y = tan(x)
215(2)
Graph of y = cot(x)
217(2)
Graph of y = sec(x)
219(1)
Graph of y = csc(x)
220(4)
The Inverse Trigonometric Functions
224(9)
The Inverse of the Sine Function
224(2)
The Inverse Cosine Function
226(1)
Inverses of Tangent, Cotangent, Secant, and Cosecant
227(3)
Compositions of Functions
230(3)
Right Triangle Trigonometry
233(9)
Trigonometric Ratios
233(1)
Right Triangles
234(2)
Solving a Right Triangle
236(1)
Applications
237(5)
Identities
242(11)
Pythagorean Identities
242(1)
Odd and Even Identities
243(1)
Sum and Difference Identities
243(1)
Cofunction Identities
244(1)
Double-Angle and Half-Angle Identities
245(2)
Product and Sum Identities
247(2)
The Function y = asinx + bcosx
249(4)
Conditional Trigonometric Equations
253(11)
Cosine Equations
253(2)
Sine Equations
255(1)
Tangent Equations
256(1)
Equations Involving Multiple Angles
257(1)
More Complicated Equations
258(3)
Modeling Projectile Motion
261(3)
The Law of Sines and the Law of Cosines
264(20)
Oblique Triangles
264(1)
The Law of Sines
264(2)
The Ambiguous Case (SSA)
266(3)
The Law of Cosines
269(3)
Bearing
272(5)
Highlights
277(2)
Chapter 3 Review Exercises
279(4)
Concepts of Calculus: Area of a circle and π
283(1)
Exponential and Logarithmic Functions
284(44)
Exponential Functions and Their Applications
285(11)
Exponential Functions
285(1)
Domain of Exponential Functions
285(1)
Graphing Exponential Functions
286(3)
The Exponential Family of Functions
289(2)
Exponential Equations
291(1)
The Compound Interest Model
291(2)
Continuous Compounding and the Number e
293(3)
Logarithmic Functions and Their Applications
296(10)
Logarithmic Functions
296(2)
Graphs of Logarithmic Functions
298(1)
The Logarithmic Family of Functions
299(1)
Logarithmic and Exponential Equations
300(3)
Applications
303(3)
Rules of Logarithms
306(8)
The Product Rule for Logarithms
306(1)
The Quotient Rule for Logarithms
307(1)
The Power Rule for Logarithms
307(1)
The Inverse Rules
308(1)
Using the Rules
309(2)
The Base Change Formula
311(3)
More Equations and Applications
314(14)
Logarithmic Equations
314(1)
Exponential Equations
315(2)
Strategy for Solving Equations
317(1)
Radioactive Dating
317(2)
Newton's Model for Cooling
319(1)
Paying off a Loan
320(3)
Highlights
323(1)
Chapter 4 Review Exercises
324(3)
Concepts of Calculus: Evaluating transcendental functions
327(1)
Conic Sections, Polar Coordinates, and Parametric Equations
328(58)
The Parabola
329(9)
The Geometric Definition
329(1)
Developing the Equation
330(1)
The Standard Equation of a Parabola
331(1)
Graphing a Parabola
332(1)
Parabolas Opening to the Left or Right
333(2)
Applications
335(3)
The Ellipse and the Circle
338(10)
Definition of Ellipse
338(1)
The Equation of the Ellipse
339(2)
Graphing an Ellipse Centered at the Origin
341(2)
Translations of Ellipses
343(1)
The Circle
344(1)
Applications
344(4)
The Hyperbola
348(14)
The Definition
349(1)
Developing the Equation
350(1)
Graphing a Hyperbola Centered at (0,0)
351(4)
Hyperbolas Centered at (h,k)
355(2)
Finding the Equation of a Hyperbola
357(1)
Classifying the Conics
358(4)
Polar Equations
362(10)
Polar Coordinates
362(1)
Polar-Rectangular Conversions
363(1)
Polar Equations
364(3)
Converting Equations
367(5)
Polar Equations of the Conics
372(4)
Alternative Definition of the Conics
372(1)
Polar Equations of the Conics
372(2)
Equivalency of the Definitions
374(2)
Parametric Equations
376(10)
Graphs of Parametric Equations
376(1)
Eliminating the Parameter
377(1)
Writing Parametric Equations
378(3)
Highlights
381(1)
Chapter 5 Review Exercises
382(3)
Concepts of Calculus: The reflection property of a parabola
385(1)
APPENDIX A BASIC ALGEBRA REVIEW
386
A.1 Exponents and Radicals
386(10)
Exponential Expressions
386(1)
Negative Integral Exponents
387(1)
Rules of Exponents
388(1)
Roots
389(1)
Rational Exponents
389(2)
Radical Notation
391(1)
The Product and Quotient Rules for Radicals
392(1)
Simplified Form and Rationalizing the Denominator
393(1)
Operations with Radical Expressions
394(2)
A.2 Polynomials
396(6)
Definitions
396(1)
Naming and Evaluating Polynomials
397(1)
Addition and Subtraction of Polynomials
397(1)
Multiplication of Polynomials
398(1)
Using FOIL
399(1)
Special Products
399(1)
Division of Polynomials
400(2)
A.3 Factoring Polynomials
402(5)
Factoring out the Greatest Common Factor
402(1)
Factoring by Grouping
403(1)
Factoring ax2 + bx + c
403(1)
Factoring the Special Products
404(1)
Factoring the Difference and Sum of Two Cubes
405(1)
Factoring Completely
406(1)
A.4 Rational Expressions
407
Reducing
407(2)
Multiplication and Division
409(1)
Building up the Denominator
410(1)
Addition and Subtraction
411
Answers to Selected Exercises 1(1)
Credits 1(1)
Index 1


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