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# Precalculus : Enhanced with Graphing Utilities

**by**Sullivan, Michael

2nd

### 9780130206923

013020692X

Hardcover

12/1/1999

Prentice Hall

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## Summary

For courses in College Algebra, Algebra & Trigonometry, Precalculus, and Trigonometry which requires student use of a graphing calculator. Using the graphing utility to enhance mathematics, not replace it, this text approaches technology as a tool to solve problems, motivate concepts, and explore ideas. Many problems are solved using both algebra and a graphing utility, with the benefits of each illustrated. Throughout, applications and examples using real data enable students to make connections between the mathematics learned and familiar situations. The authors' user-friendly approach helps students develop the skills needed to succeed in subsequent mathematics courses.

## Table of Contents

(NOTE: Each chapter concludes with *Chapter Review.*) ** 1. Graphs. **

Rectangular Coordinates; Graphing Utilities; Scatter Diagrams. Graphs of Equations. Solving Equations. Setting Up Equations; Applications. Solving Inequalities. Lines. Circles.

**2. Function and Models.**

Functions. Linear Functions and Models. Characteristics of Functions; Library of Functions. Graphing Techniques: Transformations. Operations on Functions; Composite Functions. Mathematical Models; Constructing Functions.

**3. Polynomial and Rational Functions.**

Quadratic Functions and Models. Power Functions and Models. Polynomial Functions and Models. The Real Zeros of a Polynomial Function. Complex Numbers; Quadratic Equations with a Negative Discriminant. Complex Zeros; Fundamental Theorem of Algebra. Rational Functions. Polynomial and Rational Inequalities.

**4. 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.

**5. Trigonometric Functions.**

Angles and Their Measure. Trigonometric Functions: Unit Circle Approach. Properties of the Trigonometric Functions. Right Triangle Trigonometry. Graphs of Trigonometric Functions. Sinusoidal Graphs; Sinusoidal Curve Fitting.

**6. Analytic Trigonometry.**

Trigonometric Identities. Sum and Difference Formulas. Double-Angle and Half -Angle Formulas. Product-to-Sum and Sum-to-Product Formulas. The Inverse Trigonometric Functions. Trigonometric Equations (I). Trigonometric Equations (II).

**7. Applications of Trigonometric Functions.**

Solving Right Triangles. The Law of Sines. The Law of Cosines. The Area of a Triangle. Simple Harmonic Motion; Damped Motion.

**8. Polar Coordinates; Vectors.**

Polar Coordinates. Polar Equations and Graphs. The Complex Plane; Demoivre's Theorem. Vectors. The Dot Product. Vectors in Space.

**9. 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.

**10. 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. Partial Fraction Decomposition. Systems of Nonlinear Equations. Systems of Linear Inequalities; Linear Programming.

**11. Sequences; Induction; The Binomial Theorem.**

Sequences. Arithmetic Sequences. Geometric Sequences; Geometric Series. Mathematical Induction. The Binomial Theorem.

**12. Counting and Probability.**

Sets and Counting. Permutations and Combinations. Probability of Equally Liked Outcomes. Analyzing Univariate Data; Obtaining Probabilities from Data.

**13. A Preview of Calculus: The Limit and the Derivative of a Function.**

Finding Limits Using Tables and Graphs. Algebra Techniques for Finding Limits. One-Sided Limits; Continuous Functions. The Tangent Problem; The Derivative.

**Appendix Review.**

Topics from Algebra and Geometry. Completing the Square; The Quadratic Formula. Polynomials. Polynomial Division. Rational Expressions. Radicals; Rational Exponents.

**Answers.**

**Index.**