Algebra & Trigonometry Enhanced With Graphing Utilities

9780130659125

0130659126

(NOTE: Each chapter concludes with Chapter Review.) R. Review. Real Numbers. Algebra Review. Geometry Review. Integer Exponents. Polynomials. Factoring Polynomials. Rational Expressions. Square Roots; Radicals. Rational Exponents. Chapter Review. Chapter Projects. 1. Graphs. Rectangular Coordinates; Graphing Utilities. Introduction to Graphing Equations. Solving Equations Using a Graphing Utility; Linear and Quadratic Equations. Setting up Equations; Applications. Radical Equations; Equations Quadratic in Form; Absolute Value Equations. Solving Inequalities. Lines. Circles. Chapter Projects. 2. Linear and Quadratic Functions. Functions. Linear Functions and Models. Quadratic Functions. Quadratic Models. Chapter Projects. Cumulative Review. 3. Functions and Their Graphs. Symmetry; Graphing Key Equations. Properties of Functions. Library of Functions; Piecewise-Defined Functions. Graphing Techniques: Transformations. Operations on Functions; Composite Functions. Mathematical Models: Constructing Functions. Chapter Projects. Cumulative Review. 4. Polynomial and Rational Functions. Power Functions and Models. Polynomial Functions and Models. Rational Functions I. Rational Functions II: Analyzing Graphs. Polynomial and Rational Inequalities. Chapter Projects. Cumulative Review. 5. The Zeros of a Polynomial Function. Synthetic Division. The Real Zeros of a Polynomial Function. Complex Numbers; Quadratic Equations with a Negative Discriminant. Complex Zeros; Fundamental Theorem of Algebra. Chapter Projects. Cumulative Review. 6. Exponential and Logarithmic Functions. One-to-One Functions; Inverse Functions. Exponential Functions. Logarithmic Functions. Properties of Logarithms. Logarithmic and Exponential Equations. Compound Interest. Growth and Decay. Exponential, Logarithmic, and Logistic Curve Fitting. Chapter Projects. Cumulative Review. 7. Systems of Equations and Inequalities. Systems of Linear Equations: Two Equations Containing Two Variables. Systems of Linear Equations: Three Equations Containing Three Variables. Systems of Linear Equations: Matrices. Systems of Linear Equations: Determinants. Matrix Algebra. Systems of Linear Inequalities; Linear Programming. Partial Fraction Decomposition. Chapter Projects. Cumulative Review. 8. Trigonometric Functions. Angles and Their Measure. Right Triangle Trigonometry. Computing the Values of Trigonometric Functions of Given Angles. Trigonometric Functions of General Angles. Properties of the Trigonometric Functions; Unit Circle Approach. Graphs of the Sine and Cosine Functions. Graphs of the Tangent, Cotangent, Secant, and Cosecant Functions. Phase Shifts; Sinusoidal Curve Fitting. Chapter Projects. Cumulative Review. 9. Analytic Trigonometry. The Inverse Sine, Cosine, and Tangent Functions. The Inverse Trigonometric Functions (continued). Trigonometric Identities. Sum and Difference Formulas. Double-angle and Half-angle Formulas. Product-to-Sum and Sum-to-Product Formulas. Trigonometric Equations I. Trigonometric Equations II. Chapter Projects. Cumulative Review. 10. Applications of Trigonometric Functions. Applications Involving Right Triangles. Law of Sines. Law of Cosines. Area of a Triangle. Simple Harmonic Motion; Damped Motion; Combining Waves. Chapter Projects. Cumulative Review. 11. Polar Coordinates; Vectors. Polar Coordinates. Polar Equations and Graphs. The Complex Plane; DeMoivre''s Theorem. Vectors. The Dot Product. Chapter Projects. Cumulative Review. 12. Analytic Geometry. Conics. The Parabola. The Ellipse. The Hyperbola. Rotation of Axes; General Form of a Conic. Polar Equations of Conics. Plane Curves and Parametric Equations. Systems of Nonlinear Equations. Chapter Projects. Cumulative Review. 13. Sequences; Induction; the Binomial Theorem. Sequences. Arithmetic Sequences. Geometric Sequences; Geometric Series. Mathematical Induction. The Binomial Theorem. Chapter Projects. Cumulative Review. 14. Counting and Probability. Sets and Counting. Permutations and Combinations. Probability of Equally Likely Outcomes. Obtaining Probabilities from Data. Chapter Projects. Cumulative Review. Answers. Index.