Precalculus

1. Equations, Inequalities, and Functions.


Solving Equations and Inequalities in One Variable Algebraically. Rectangular Coordinates; Graphing Utilities. Introduction to Graphing Equations. Symmetry; Graphing Key Equations; Circles. Solving Equations and Inequalities in One Variable Using a Graphing Utility. Introduction to Functions. The Graph of a Function. Properties of Functions.



2. Linear Functions and Models.


Properties of Linear Functions. Equations of Lines; Building Linear Functions. Setting Up Linear Equations; Applications. Building Linear Functions from Data.



3. Quadratic Functions and Models.


Quadratic Equations. Properties of Quadratic Functions. Quadratic Inequalities. Building Quadratic Functions. Complex Numbers; Quadratic Equations with a Negative Discriminant.



4. Additional Functions and Models.


Radical Equations; Absolute Value Equations; Absolute Value Inequalities. Library of Functions; Piecewise-Defined Functions. Graphing Techniques: Transformations. Models Involving the Square Root Function and Piecewise-Defined Functions.



5. Polynomial and Rational Functions.


Power Functions and Models. Polynomial Functions and Models. Rational Functions I. Rational Functions II. Polynomial and Rational Inequalities. The Real Zeros of a Polynomial Function. Complex Zeros; Fundamental Theorem of Algebra.



6. Exponential and Logarithmic Functions.


Composite Functions. Inverse Functions. Exponential Functions. Logarithmic Functions. Properties of Logarithms. Logarithmic and Exponential Equations. Compound Interest. Growth and Decay. Logistic Growth and Decay. Exponential, Logarithmic and Logistic Modeling.



7. Trigonometric Functions.


Angles and Their Measure. Trigonometric Functions: Unit Circle Approach. Properties of the Trigonometric Functions. Graphs of the Sine and Cosine Functions: Sinusoidal Graphs. Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions. Phase Shifts: Sinusoidal Curve Fitting.



8. 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.



9. Applications of Trigonometric Functions.


Right Triangle Trigonometry. Law of Sines. Law of Cosines. Area of a Triangle. Simple Harmonic Motion; Damped Motion; Combining Waves.



10. Polar Coordinates; Vectors.


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



11. 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.



12. 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 Inequalities. Linear Programming.



13. Sequences; Induction; The Binomial Theorem.


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



14. Counting and Probability.


Sets and Counting. Permutations and Combinations. Probability of Equally Likely Outcomes. Obtaining Probabilities from Data.



15. A Preview of Calculus: The Limit, Derivative, and Integral of a Function.


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



Appendix Review.


Algebra Review. Geometry Review. Polynomials. Rational Expressions. Polynomial Division; Synthetic Division. nth Roots; Rational Exponents.



Answers.


Index.