College Algebra Essentials

Title
Contents
CHAPTER R A Review of Basic Concepts and Skills
	R.1 The Language, Notation, and Numbers of Mathematics
		R.2 Algebraic Expressions and the Properties of Real Numbers
			R.3 Exponents, Scientific Notation, and a Review of Polynomials
				R.4 Factoring Polynomials
					R.5 Rational Expressions
					R.6 Radicals and Rational Exponents
						Overview of Chapter R: Important Definitions, Properties, Formulas, and Relationships
							Practice Test
CHAPTER 1 Equations and Inequalities
	1.1 Linear Equations, Formulas, and Problem Solving
		Technology Highlight: Using a Graphing Calculator as an Investigative Tool
			1.2 Linear Inequalities in One Variable
				1.3 Absolute Value Equations and Inequalities
					Technology Highlight: Absolute Value Equations and Inequalities
						Mid-Chapter Check
						Reinforcing Basic Concepts: Using Distance to Understand Absolute Value Equations and Inequalities
				1.4 Complex Numbers
				1.5 Solving Quadratic Equations
					Technology Highlight: The Discriminant
				1.6 Solving Other Types of Equations
					Summary and Concept Review
						Mixed Review
						Practice Test
						Calculator Exploration and Discovery: Evaluating Expressions and Looking for Patterns
						Strengthening Core Skills: An Alternative Method for Checking Solutions to Quadratic Equations
CHAPTER 2 Relations, Functions, and Graphs
	2.1 Rectangular Coordinates; Graphing Circles and Other Relations
		Technology Highlight: The Graph of a Circle
			2.2 Graphs of Linear Equations
				Technology Highlight: Linear Equations, Window Size, and Friendly Windows
				2.3 Linear Graphs and Rates of Change
				2.4 Functions, Function Notation, and the Graph of a Function
					Mid-Chapter Check
						Reinforcing Basic Concepts: The Various Forms of a Linear Equation
		2.5 Analyzing the Graph of a Function
			Technology Highlight: Locating Zeroes, Maximums, and Minimums
		2.6 The Toolbox Functions and Transformations
			Technology Highlight: Function Families
		2.7 Piecewise-Defined Functions
			Technology Highlight: Piecewise-Defined Functions
		2.8 The Algebra and Composition of Functions
			Technology Highlight: Composite Functions
				Summary and Concept Review
					Mixed Review
					Practice Test
					Calculator Exploration and Discovery: Using a Simple Program to Explore Transformations
					Strengthening Core Skills: Transformations via Composition
					Cumulative Review: Chapters 1–2
					Modeling with Technology I: Linear and Quadratic Equation Models
CHAPTER 3 Polynomial and Rational Functions
	3.1 Quadratic Functions and Applications
		Technology Highlight: Estimating Irrational Zeroes
	3.2 Synthetic Division; The Remainder and Factor Theorems
	3.3 The Zeroes of Polynomial Functions
		Technology Highlight: The Intermediate Value Theorem and Split Screen Viewing
	3.4 Graphing Polynomial Functions
		Mid-Chapter Check
			Reinforcing Basic Concepts: Approximating Real Zeroes
	3.5 Graphing Rational Functions
		Technology Highlight: Rational Functions and Appropriate Domains
	3.6 Additional Insights into Rational Functions
		Technology Highlight: Removable Discontinuities
	3.7 Polynomial and Rational Inequalities
		Technology Highlight: Polynomial and Rational Inequalities
	3.8 Variation: Function Models in Action
		Summary and Concept Review
			Mixed Review
				Practice Test
				Calculator Exploration and Discovery: Complex Zeroes, Repeated Zeroes, and Inequalities
				Strengthening Core Skills: Solving Inequalities Using the Push Principle
				Cumulative Review: Chapters 1–3
CHAPTER 4 Exponential and Logarithmic Functions
	4.1 One-to-One and Inverse Functions
		Technology Highlight: Investigating Inverse Functions
			4.2 Exponential Functions
				Technology Highlight: Solving Exponential Equations Graphically
				4.3 Logarithms and Logarithmic Functions
					Mid-Chapter Check
						Reinforcing Basic Concepts: Linear and Logarithmic Scales
				4.4 Properties of Logarithms; Solving Exponential Logarithmic Equations
				4.5 Applications from Business, Finance, and Science
					Technology Highlight: Exploring Compound Interest
						Summary and Concept Review
						Mixed Review
						Practice Test
						Calculator Exploration and Discovery: Investigating Logistic Equations
						Strengthening Core Skills: Understanding Properties of Logarithms
						Cumulative Review: Chapters 1–4
						Modeling with Technology II: Exponential, Logarithmic, and Other Regression Models
CHAPTER 5 Systems of Equations and Inequalities
	5.1 Linear Systems in Two Variables with Applications
		Technology Highlight: Solving Systems Graphically
			5.2 Linear Systems in Three Variables with Applications
				Technology Highlight: More on Parameterized Solutions
					Mid-Chapter Check
						Reinforcing Basic Concepts: Window Size and Graphing Technology
				5.3 Nonlinear Systems of Equations and Inequalities
				5.4 Systems of Inequalities and Linear Programming
					Technology Highlight: Systems of Linear Inequalities
						Summary and Concept Review
						Mixed Review
						Practice Test
						Calculator Exploration and Discovery: Optimal Solutions and Linear Programming
						Strengthening Core Skills: Understanding Why Elimination and Substitution “Work”
						Cumulative Review: Chapters 1–5
Appendix I More on Synthetic Division
Appendix ii Proof Positive—A Selection of Proofs from College Algebra
Index