Precalculus : graphs and models : a right triangle approach

Cover
Title Page
Copyright Page
Acknowledgments
Contents
Preface
To the Student
Interactive Figures Index
R: Basic Concepts of Algebra
	R.1 The Real-Number System
		Real Numbers
		Interval Notation
		Properties of the Real Numbers
		Absolute Value
	R.2 Integer Exponents, Scientific Notation, and Order of Operations
		Integers as Exponents
		Scientific Notation
		Order of Operations
	R.3 Addition, Subtraction, and Multiplication of Polynomials
		Polynomials
		Addition and Subtraction
		Multiplication
	R.4 Factoring
		Terms with Common Factors
		Factoring by Grouping
		Trinomials of the Type x[sup(2)] + bx + c
		Trinomials of the Type ax[sup(2)] + bx + c, a ≠ 1
		Special Factorizations
	R.5 The Basics of Equation Solving
		Linear Equations and Quadratic Equations
		Formulas
	R.6 Rational Expressions
		The Domain of a Rational Expression
		Simplifying, Multiplying, and Dividing Rational Expressions
		Adding and Subtracting Rational Expressions
		Complex Rational Expressions
	R.7 Radical Notation and Rational Exponents
		Simplifying Radical Expressions
		An Application
		Rationalizing Denominators or Numerators
		Rational Exponents
	Study Guide
	Review Exercises
	Chapter Test
1 Graphs, Functions, and Models
	1.1 Introduction to Graphing
		Graphs
		Solutions of Equations
		Graphs of Equations
		The Distance Formula
		Midpoints of Segments
		Circles
		VISUALIZING THE GRAPH
	1.2 Functions and Graphs
		Functions
		Notation for Functions
		Graphs of Functions
		Finding Domains of Functions
		Visualizing Domain and Range
		Applications of Functions
	1.3 Linear Functions, Slope, and Applications
		Linear Functions
		The Linear Function f (x) = mx + b and Slope
		Applications of Slope
		Slope–Intercept Equations of Lines
		Graphing f (x) = mx + b Using m and b
		Applications of Linear Functions
		VISUALIZING THE GRAPH
		MID-CHAPTER MIXED REVIEW
	1.4 Equations of Lines and Modeling
		Slope–Intercept Equations of Lines
		Point–Slope Equations of Lines
		Parallel Lines
		Perpendicular Lines
		Mathematical Models
		Curve Fitting
		Linear Regression
	1.5 Linear Equations, Functions, Zeros, and Applications
		Linear Equations
		Applications Using Linear Models
		Zeros of Linear Functions
	1.6 Solving Linear Inequalities
		Linear Inequalities
		Compound Inequalities
		An Application
	Study Guide
	Review Exercises
	Chapter Test
2 More on Functions
	2.1 Increasing, Decreasing, and Piecewise Functions; Applications
		Increasing, Decreasing, and Constant Functions
		Relative Maximum and Minimum Values
		Applications of Functions
		Functions Defined Piecewise
	2.2 The Algebra of Functions
		The Algebra of Functions: Sums, Differences, Products, and Quotients
		Difference Quotients
	2.3 The Composition of Functions
		The Composition of Functions
		Decomposing a Function as a Composition
		MID-CHAPTER MIXED REVIEW
	2.4 Symmetry
		Symmetry
		Even Functions and Odd Functions
	2.5 Transformations
		Transformations of Functions
		Vertical Translations and Horizontal Translations
		Reflections
		Vertical and Horizontal Stretchings and Shrinkings
		VISUALIZING THE GRAPH
	2.6 Variation and Applications
		Direct Variation
		Inverse Variation
		Combined Variation
	Study Guide
	Review Exercises
	Chapter Test
3 Quadratic Functions and Equations; Inequalities
	3.1 The Complex Numbers
		The Complex-Number System
		Addition and Subtraction
		Multiplication
		Conjugates and Division
	3.2 Quadratic Equations, Functions, Zeros, and Models
		Quadratic Equations and Quadratic Functions
		Completing the Square
		Using the Quadratic Formula
		The Discriminant
		Equations Reducible to Quadratic
		Applications
	3.3 Analyzing Graphs of Quadratic Functions
		Graphing Quadratic Functions of the Type f (x) = a (x – h)[sup(2)] + k
		Graphing Quadratic Functions of the Type f (x) = ax2 + bx + c , a ≠ 0
		Applications
		VISUALIZING THE GRAPH
		MID-CHAPTER MIXED REVIEW
	3.4 Solving Rational Equations and Radical Equations
		Rational Equations
		Radical Equations
	3.5 Solving Equations and Inequalities with Absolute Value
		Equations with Absolute Value
		Inequalities with Absolute Value
	Study Guide
	Review Exercises
	Chapter Test
4 Polynomial Functions and Rational Functions
	4.1 Polynomial Functions and Modeling
		The Leading-Term Test
		Finding Zeros of Factored Polynomial
		Finding Real Zeros on a Calculator
		Polynomial Models
	4.2 Graphing Polynomial Functions
		Graphing Polynomial Functions
		The Intermediate Value Theorem
		VISUALIZING THE GRAPH
	4.3 Polynomial Division; The Remainder Theorem and the Factor Theorem
		Division and Factors
		The Remainder Theorem and Synthetic Division
		Finding Factors of Polynomials
		MID-CHAPTER MIXED REVIEW
	4.4 Theorems about Zeros of Polynomial Functions
		The Fundamental Theorem of Algebra
		Finding Polynomials with Given Zeros
		Zeros of Polynomial Functions with Real Coefficients
		Rational Coefficients
		Integer Coefficients and the Rational Zeros Theorem
		Descartes’ Rule of Signs
	4.5 Rational Functions
		The Domain of a Rational Function
		Asymptotes
		Applications
		VISUALIZING THE GRAPH
	4.6 Polynomial Inequalities and Rational Inequalities
		Polynomial Inequalities
		Rational Inequalities
	Study Guide
	Review Exercises
	Chapter Test
5 Exponential Functions and Logarithmic Functions
	5.1 Inverse Functions
		Inverses
		Inverses and One-to-One Functions
		Finding Formulas for Inverses
		Inverse Functions and Composition
		Restricting a Domain
	5.2 Exponential Functions and Graphs
		Graphing Exponential Functions
		Applications
		The Number e
		Graphs of Exponential Functions, Base e
	5.3 Logarithmic Functions and Graphs
		Logarithmic Functions
		Finding Certain Logarithms
		Converting Between Exponential Equations and Logarithmic Equations
		Finding Logarithms on a Calculator
		Natural Logarithms
		Changing Logarithmic Bases
		Graphs of Logarithmic Functions
		Applications
		VISUALIZING THE GRAPH
		MID-CHAPTER MIXED REVIEW
	5.4 Properties of Logarithmic Functions
		Logarithms of Products
		Logarithms of Powers
		Logarithms of Quotients
		Applying the Properties
		Simplifying Expressions of the Type log[sub(a)] a[sup(x)] and a[sup[log)][sub(a)][sup(x)]
	5.5 Solving Exponential Equations and Logarithmic Equations
		Solving Exponential Equations
		Solving Logarithmic Equations
	5.6 Applications and Models: Growth and Decay; Compound Interest
		Population Growth
		Interest Compounded Continuously
		Models of Limited Growth
		Exponential Decay
		Exponential and Logarithmic Curve Fitting
	Study Guide
	Review Exercises
	Chapter Test
6 The Trigonometric Functions
	6.1 Trigonometric Functions of Acute Angles
		The Trigonometric Ratios
		The Six Functions Related
		Function Values of 30°, 45°, and 60°
		Function Values of Any Acute Angle
		Cofunctions and Complements
	6.2 Applications of Right Triangles
		Solving Right Triangles
		Applications
	6.3 Trigonometric Functions of Any Angle
		Angles, Rotations, and Degree Measure
		Trigonometric Functions of Angles or Rotations
		The Six Functions Related
		Terminal Side on an Axis
		Reference Angles: 30°, 45°, and 60°
		Function Values for Any Angle
		MID-CHAPTER MIXED REVIEW
	6.4 Radians, Arc Length, and Angular Speed
		Distances on the Unit Circle
		Radian Measure
		Arc Length and Central Angles
		Linear Speed and Angular Speed
	6.5 Circular Functions: Graphs and Properties
		Reflections on the Unit Circle
		Finding Function Values
		Graphs of the Sine and Cosine Functions
		Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
	6.6 Graphs of Transformed Sine Functions and Cosine Functions
		Variations of Basic Graphs
		Graphs of Sums: Addition of Ordinates
		Damped Oscillation: Multiplication of Ordinates
		VISUALIZING THE GRAPH
	Study Guide
	Review Exercises
	Chapter Test
7 Trigonometric Identities, Inverse Functions, and Equations
	7.1 Identities: Pythagorean and Sum and Difference
		Pythagorean Identities
		Simplifying Trigonometric Expressions
		Sum and Difference Identities
	7.2 Identities: Cofunction, Double-Angle, and Half-Angle
		Cofunction Identities
		Double-Angle Identities
		Half-Angle Identities
	7.3 Proving Trigonometric Identities
		The Logic of Proving Identities
		Proving Identities
		Product-to-Sum and Sum-to-Product Identities
		MID-CHAPTER MIXED REVIEW
	7.4 Inverses of the Trigonometric Functions
		Restricting Ranges to Define Inverse Functions
		Composition of Trigonometric Functions and Their Inverses
	7.5 Solving Trigonometric Equations
		VISUALIZING THE GRAPH
	Study Guide
	Review Exercises
	Chapter Test
8 Applications of Trigonometry
	8.1 The Law of Sines
		Solving Oblique Triangles
		The Law of Sines
		Solving Triangles (AAS and ASA)
		Solving Triangles (SSA)
		The Area of a Triangle
	8.2 The Law of Cosines
		The Law of Cosines
		Solving Triangles (SAS)
		Solving Triangles (SSS)
	8.3 Complex Numbers: Trigonometric Notation
		Graphical Representation
		Trigonometric Notation for Complex Numbers
		Multiplication and Division with Trigonometric Notation
		Powers of Complex Numbers
		Roots of Complex Numbers
		MID-CHAPTER MIXED REVIEW
	8.4 Polar Coordinates and Graphs
		Polar Coordinates
		Polar Equations and Rectangular Equations
		Graphing Polar Equations
		VISUALIZING THE GRAPH
	8.5 Vectors and Applications
		Vectors
		Vector Addition
		Applications
		Components
	8.6 Vector Operations
		Position Vectors
		Operations on Vectors
		Unit Vectors
		Direction Angles
		Angle Between Vectors
		Forces in Equilibrium
	Study Guide
	Review Exercises
	Chapter Test
9 Systems of Equations and Matrices
	9.1 Systems of Equations in Two Variables
		Solving Systems of Equations Graphically
		The Substitution Method
		The Elimination Method
		Applications
		VISUALIZING THE GRAPH
	9.2 Systems of Equations in Three Variables
		Solving Systems of Equations in Three Variables
		Applications
		Mathematical Models and Applications
	9.3 Matrices and Systems of Equations
		Matrices and Row-Equivalent Operations
		Gaussian Elimination with Matrices
		Gauss–Jordan Elimination
	9.4 Matrix Operations
		Matrix Addition and Subtraction
		Scalar Multiplication
		Products of Matrices
		Matrix Equations
		MID-CHAPTER MIXED REVIEW
	9.5 Inverses of Matrices
		The Identity Matrix
		The Inverse of a Matrix
		Solving Systems of Equations
	9.6 Determinants and Cramer’s Rule
		Determinants of Square Matrices
		Evaluating Determinants Using Cofactors
		Cramer’s Rule
	9.7 Systems of Inequalities and Linear Programming
		Graphs of Linear Inequalities
		Systems of Linear Inequalities
		Applications: Linear Programming
	9.8 Partial Fractions
		Partial Fraction Decompositions
	Study Guide
	Review Exercises
	Chapter Test
10 Analytic Geometry Topics
	10.1 The Parabola
		Parabolas
		Finding Standard Form by Completing the Square
		Applications
	10.2 The Circle and the Ellipse
		Circles
		Ellipses
		Applications
	10.3 The Hyperbola
		Standard Equations of Hyperbolas
		Applications
	10.4 Nonlinear Systems of Equations and Inequalities
		Nonlinear Systems of Equations
		Modeling and Problem Solving
		Nonlinear Systems of Inequalities
		VISUALIZING THE GRAPH
		MID-CHAPTER MIXED REVIEW
	10.5 Rotation of Axes
		Rotation of Axes
		The Discriminant
	10.6 Polar Equations of Conics
		Polar Equations of Conics
		Converting from Polar Equations to Rectangular Equations
		Finding Polar Equations of Conics
	10.7 Parametric Equations
		Graphing Parametric Equations
		Determining a Rectangular Equation for Given Parametric Equations
		Determining Parametric Equations for a Given Rectangular Equation
		Applications
	Study Guide
	Review Exercises
	Chapter Test
11 Sequences, Series, and Combinatorics
	11.1 Sequences and Series
		Sequences
		Finding the General Term
		Sums and Series
		Sigma Notation
		Recursive Definitions
	11.2 Arithmetic Sequences and Series
		Arithmetic Sequences
		Sum of the First n Terms of an Arithmetic Sequence
		Applications
	11.3 Geometric Sequences and Series
		Geometric Sequences
		Sum of the First n Terms of a Geometric Sequence
		Infinite Geometric Series
		Applications
		VISUALIZING THE GRAPH
	11.4 Mathematical Induction
		Proving Infinite Sequences of Statements
		MID-CHAPTER MIXED REVIEW
	11.5 Combinatorics: Permutations
		Permutations
		Factorial Notation
		Permutations of n Objects Taken k at a Time
		Permutations of Sets with Nondistinguishable Objects
	11.6 Combinatorics: Combinations
		Combinations
	11.7 The Binomial Theorem
		Binomial Expansions Using Pascal’s Triangle
		Binomial Expansion Using Combination Notation
		Finding a Specific Term
		Total Number of Subsets
	11.8 Probability
		Experimental Probability and Theoretical Probability
		Computing Experimental Probabilities
		Theoretical Probability
	Study Guide
	Review Exercises
	Chapter Test
Photo Credits
Answers
Index
	A
	B
	C
	D
	E
	F
	G
	H
	I
	J
	K
	L
	M
	N
	O
	P
	Q
	R
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	T
	U
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	W
	X
	Y
	Z
Index of Applications