Precalculus

(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.