Algebra and Trigonometry

CHAPTER P PREREQUISITES. P.1. Real Numbers. P.2. Exponents and Radicals. P.3. Polynomials and Factoring. P.4. Rational Expressions. P.5. The Cartesian Plane. P.6. Representing Data Graphically. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. 1. FUNCTIONS AND THEIR GRAPHS. Introduction to Library of Functions.1.1 Graphs of Equations. 1.2 Lines in the Plane. 1.3 Functions. 1.4 Graphs of Functions.1.5 Shifting, Reflecting, and Stretching Graphs. 1.6 Combinations of Functions. 1.7 Inverse Functions. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. 2. SOLVING EQUATIONS AND INEQUALITIES. 2.1 Linear Equations and Problem Solving. 2.2 Solving Equations Graphically. 2.3 Complex Numbers. 2.4 Solving Quadratic Equations Algebraically. 2.5 Solving Other Types of Equations Algebraically. 2.6 Solving Inequalities Algebraically and Graphically. 2.7 Linear Models and Scatter Plots. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test: Chapters P-2. Proofs in Mathematics. Progressive Summary (Ch P-2). 3. POLYNOMIAL AND RATIONAL FUNCTIONS. 3.1 Quadratic Functions. 3.2 Polynomial Functions of Higher Degree. 3.3 Real Zeros of Polynomial Functions. 3.4 The Fundamental Theorem of Algebra. 3.5 Rational Functions and Asymptotes. 3.6 Graphs of Rational Functions. 3.7 Quadratic Models. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. 4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. 4.1 Exponential Functions and Their Graphs . 4.2 Logarithmic Functions and Their Graphs. 4.3 Properties of Logarithms. 4.4 Solving Exponential and Logarithmic Equations. 4.5 Exponential and Logarithmic Models. 4.6 Nonlinear Models. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test: Chapters 3-4. Proofs in Mathematics. Progressive Summary (Ch P-4). 5. TRIGONOMETRIC FUNCTIONS. 5.1 Angles and Their Measure. 5.2 Right Triangle Trigonometry. 5.3 Trigonometric Functions of Any Angle. 5.4 Graphs of Sine and Cosine Functions. 5.5 Graphs of Other Trigonometric Functions. 5.6 Inverse Trigonometric Functions. 5.7 Applications and Models. Chapter Summary. Review Exercises. Chapter Test. Library of Parent Functions Review. Proofs in Mathematics. 6. ANALYTIC TRIGONOMETRY. 6.1 Using Fundamental Identities. 6.2 Verifying Trigonometric Identities. 6.3 Solving Trigonometric Equations. 6.4 Sum and Difference Formulas. 6.5 Multiple-Angle and Product-to-Sum Formulas. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. 7. ADDITIONAL TOPICS IN TRIGONOMETRY. 7.1 Law of Sines. 7.2 Law of Cosines. 7.3 Vectors in the Plane. 7.4 Vectors and Dot Products. 7.5 Trigonometric Form of a Complex Number. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test: Chapters 5-7. Proofs in Mathematics. Progressive Summary (Ch P-7). 8. LINEAR SYSTEMS AND MATRICES. 8.1 Solving Systems of Equations. 8.2 Systems of Linear Equations in Two Variables. 8.3 Multivariable Linear Systems. 8.4 Matrices and Systems of Equations. 8.5 Operations with Matrices. 8.6 The Inverse of a Square Matrix. 8.7 The Determinant of a Square Matrix. 8.8 Applications of Matrices and Determinants. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. 9. SEQUENCES, SERIES, AND PROBABILITY. 9.1 Sequences and Series. 9.2 Arithmetic Sequences and Partial Sums. 9.3 Geometric Sequences and Series. 9.4 The Binomial Theorem. 9.5 Counting Principles. 9.6 Probability. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. 10. TOPICS IN ANALYTIC GEOMETRY. 10.1 Circles and Parabolas. 10.2 Ellipses. 10.3 Hyperbolas. 10.4 Parametric Equations. 10.5 Polar Coordinates. 10.6 Graphs of Polar Equations. 10.7 Polar Equations of Conics. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test: Chapters 8-10. Proofs in Mathematics. Progressive Summary (Ch P-10). Appendix A: Technology Support Guide. Appendix B: Concepts in Statistics (WEB only). B.1 Measures of Central Tendency and Dispersion. B.2 Least