Graphical Approach to Precalculus with Limits, A

<ol> <li><strong>Linear Functions, Equations, and Inequalities</strong> <ul> <li>1.1 Real Numbers and the Rectangular Coordinate System</li> <li>1.2 Introduction to Relations and Functions <ul> <li>Reviewing Basic Concepts (Sections 1.1–1.2)</li> </ul></li> <li>1.3 Linear Functions</li> <li>1.4 Equations of Lines and Linear Models <ul> <li>Reviewing Basic Concepts (Sections 1.3–1.4)</li> </ul></li> <li>1.5 Linear Equations and Inequalities</li> <li>Unifying Linear Functions</li> <li>1.6 Applications of Linear Functions <ul> <li>Reviewing Basic Concepts (Sections 1.5–1.6)</li> </ul></li> <li>Summary</li> <li>Review Exercises</li> <li>Test</li> </ul></li> <li><strong>Analysis of Graphs of Functions</strong> <ul> <li>2.1 Graphs of Basic Functions and Relations; Symmetry</li> <li>2.2 Vertical and Horizontal Shifts of Graphs</li> <li>2.3 Stretching, Shrinking, and Reflecting Graphs <ul> <li>Reviewing Basic Concepts (Sections 2.1–2.3)</li> </ul></li> <li>2.4 Absolute Value Functions <ul> <li>Unifying Absolute Value Functions</li> </ul></li> <li>2.5 Piecewise-Defined Functions</li> <li>2.6 Operations and Composition <ul> <li>Reviewing Basic Concepts (Sections 2.4–2.6)</li> </ul></li> <li>Summary</li> <li>Review Exercises</li> <li>Test</li> </ul></li> <li><strong>Quadratic Functions</strong> <ul> <li>3.1 Complex Numbers</li> <li>3.2 Quadratic Functions and Graphs <ul> <li>Reviewing Basic Concepts (Sections 3.1–3.2)</li> </ul></li> <li>3.3 Quadratic Equations and Inequalities <ul> <li>Unifying Quadratic Functions</li> </ul></li> <li>3.4 Applications of Quadratic Functions and Models <ul> <li>Reviewing Basic Concepts (Sections 3.3–3.4)</li> </ul></li> <li>Summary</li> <li>Review Exercises</li> <li>Test</li> </ul></li> <li><strong>Polynomial Functions of Higher Degree</strong> <ul> <li>4.1 Graphs of Polynomial Functions</li> <li>4.2 Topics in the Theory of Polynomial Functions (I) <ul> <li>Reviewing Basic Concepts (Sections 4.1–4.2)</li> </ul></li> <li>4.3 Topics in the Theory of Polynomial Functions (II)</li> <li>4.4 Polynomial Equations, Inequalities, Applications, and Models <ul> <li>Reviewing Basic Concepts (Sections 4.3–4.4)</li> <li>Unifying Polynomial Functions</li> </ul></li> <li>Summary</li> <li>Review Exercises</li> <li>Test</li> </ul></li> <li><strong>Rational, Power, and Root Functions</strong> <ul> <li>5.1 Rational Functions and Graphs (I)</li> <li>5.2 Rational Functions and Graphs (II)</li> <li>5.3 Rational Equations, Inequalities, Models, and Applications <ul> <li>Reviewing Basic Concepts (Sections 5.1–5.3)</li> </ul></li> <li>5.4 Functions Defined by Powers and Roots</li> <li>5.5 Equations, Inequalities, and Applications Involving Root Functions <ul> <li>Reviewing Basic Concepts (Sections 5.4–5.5)</li> <li>Unifying Root Functions</li> </ul></li> <li>Summary</li> <li>Review Exercises</li> <li>Test</li> </ul></li> <li><strong>Inverse, Exponential, and Logarithmic Functions</strong> <ul> <li>6.1 Inverse Functions</li> <li>6.2 Exponential Functions <ul> <li>Unifying Exponential Functions</li> </ul></li> <li>6.3 Logarithms and Their Properties <ul> <li>Reviewing Basic Concepts (Sections 6.1¿–6.3)</li> </ul></li> <li>6.4 Logarithmic Functions</li> <li>6.5 Exponential and Logarithmic Equations and Inequalities <ul> <li>Unifying Logarithmic Functions</li> </ul></li> <li>6.6 Further Applications and Modeling with Exponential and Logarithmic Functions <ul> <li>Reviewing Basic Concepts (Sections 6.4–6.6)</li> <li>Summary Exercises on Functions: Domains, Defining Equations, and Composition</li> </ul></li> <li>Summary</li> <li>Review Exercises</li> <li>Test</li> </ul></li> <li><strong>Systems and Matrices</strong> <ul> <li>7.1 Systems of Equations</li> <li>7.2 Solution of Linear Systems in Three Variables</li> <li>7.3 Solution of Linear Systems by Row Transformations <ul> <li>Reviewing Basic Concepts (Sections 7.1–7.3)</li> </ul></li> <li>7.4 Matrix Properties and Operations</li> <li>7.5 Determinants and Cramer’s Rule</li> <li>7.6 Solution of Linear Systems by Matrix Inverses <ul> <li>Reviewing Basic Concepts (Sections 7.4–7.6)</li> </ul></li> <li>7.7 Systems of Inequalities and Linear Programming</li> <li>7.8 Partial Fractions <ul> <li>Reviewing Basic Concepts (Sections 7.7–7.8)</li> </ul></li> <li>Summary</li> <li>Review Exercises</li> <li>Test</li> </ul></li> <li><strong>Conic Sections, Nonlinear Systems, and Parametric Equations</strong> <ul> <li>8.1 Circles Revisited and Parabolas</li> <li>8.2 Ellipses and Hyperbolas <ul> <li>Reviewing Basic Concepts (Sections 8.1–8.2)</li> </ul></li> <li>8.3 The Conic Sections and Nonlinear Systems</li> <li>8.4 Introduction to Parametric Equations <ul> <li>Reviewing Basic Concepts (Sections 8.3–8.4)</li> </ul></li> <li>Summary</li> <li>Review Exercises</li> <li>Test</li> </ul></li> <li><strong>The Unit Circle and the Functions of Trigonometry</strong> <ul> <li>9.1 Angles, Arcs, and Their Measures</li> <li>9.2 The Unit Circle and Its Functions</li> <li>9.3 Graphs of the Sine and Cosine Functions</li> <li>9.4 Graphs of the Other Circular Functions</li> <li>9.5 Functions of Angles and Fundamental Angles</li> <li>9.6 Evaluating Trigonometric Functions</li> <li>9.7 Applications of Right Triangles</li> <li>9.8 Harmonic Motion</li> <li>Summary</li> <li>Review Exercises</li> <li>Test</li> </ul></li> <li><strong>Trigonometric Identities and Equations</strong> <ul> <li>10.1 Trigonometric Identities</li> <li>10.2 Sum and Difference Identities</li> <li>10.3 Further Identities</li> <li>10.4 The Inverse Circular Functions</li> <li>10.5 Trigonometric Equations and Inequalities (I)</li> <li>10.6 Trigonometric Equations and Inequalities (II) <ul> <li>Unifying Trigonometric Functions</li> </ul></li> <li>Summary</li> <li>Review Exercises</li> <li>Test</li> </ul></li> <li><strong>Applications of Trigonometry and Vectors</strong> <ul> <li>11.1 The Law of Sines</li> <li>11.2 The Law of Cosines and Area Formulas</li> <li>11.3 Vectors and Their Applications</li> <li>11.4 Trigonometric (Polar) Form of Complex Numbers</li> <li>11.5 Powers and Roots of Complex Numbers</li> <li>11.6 Polar Equations and Graphs</li> <li>11.7 More Parametric Equations</li> <li>Summary</li> <li>Review Exercises</li> <li>Test</li> </ul></li> <li><strong>Further Topics in Algebra</strong> <ul> <li>12.1 Sequences and Series</li> <li>12.2 Arithmetic Sequences and Series</li> <li>12.3 Geometric Sequences and Series <ul> <li>Reviewing Basic Concepts (Sections 9.1–9.3)</li> </ul></li> <li>12.4 Counting Theory</li> <li>12.5 The Binomial Theorem <ul> <li>Reviewing Basic Concepts (Sections 9.4–9.5)</li> </ul></li> <li>12.6 Mathematical Induction</li> <li>12.7 Probability <ul> <li>Reviewing Basic Concepts (Sections 9.6–9.7)</li> </ul></li> <li>Summary</li> <li>Review Exercises</li> <li>Test</li> </ul></li> <li><strong>Limits, Derivatives, and Definite Integrals</strong> <ul> <li>13.1 An Introduction to Limits</li> <li>13.2 Techniques for Calculating Limits</li> <li>13.3 One-Sided Limits and Limits Involving Infinity</li> <li>13.4 Tangent Lines and Derivatives</li> <li>13.5 Area and the Definite Integral</li> </ul></li> <li><strong>Review: Basic Algebraic Concepts</strong> <ul> <li>R.1 Review of Sets</li> <li>R.2 Review of Exponents and Polynomials</li> <li>R.3 Review of Factoring</li> <li>R.4 Review of Rational Expressions</li> <li>R.5 Review of Negative and Rational Exponents</li> <li>R.6 Review of Radicals</li> <li>Test</li> </ul></li> </ol> <h3>Appendices</h3> <ul> <li>A. Geometry Formulas</li> <li>B. Vectors in Space</li> <li>C. Polar Form of Conic Sections</li> <li>D. Rotation of Axes</li> </ul> <p>Instructor’s Answers</p> <p>Answers to Selected Exercises*</p> <p>Index</p> <ul> <li>*In the AIE, Instructor’s Answers replaces Answers to Selected Exercises.</li> </ul>