Graphical Approach to Precalculus with Limits, A

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

Appendices

• A. Geometry Formulas
• B. Vectors in Space
• C. Polar Form of Conic Sections
• D. Rotation of Axes

• *In the AIE, Instructor’s Answers replaces Answers to Selected Exercises.