Making the transition to calculus means being prepared to grasp bigger and more complex mathematical concepts. Precalculus: Functions and Graphs is designed to make this transition seamless, by focusing now on all the skills that you will need in the future. The foundation for success begins with preparation and Precalculus: Functions and Graphs will help you succeed in this course and beyond.
1. Equations, Inequalities, and Modeling.
Equations in One Variable.
Constructing Models to Solve Problems.
Equations and Graphs in Two Variables.
Linear Equations in Two Variables.
Scatter Diagrams and Curve Fitting. Complex Numbers.
Quadratic Equations.
Linear and Absolute Value Inequalities.
2. Functions and Graphs.
Functions.
Graphs of Relations and Functions.
Families of Functions, Transformations, and Symmetry.
Operations with Functions.
Inverse Functions.
Constructing Functions with Variation.
3. Polynomial and Rational Functions.
Quadratic Functions and Inequalities.
Zeros of Polynomial Functions. The Theory of Equations.
Miscellaneous Equations.
Graphs of Polynomial Functions.
Rational Functions and Inequalities.
4. Exponential and Logarithmic Functions.
Exponential Functions and Their Applications.
Logarithmic Functions and Their Applications.
Rules of Logarithms.
More Equations and Applications.
5. The Trigonometric Functions.
Angles and Their Measurements.
The Sine and Cosine Functions.
The Graphs of the Sine and Cosine Functions.
The Other Trigonometric Functions and Their Graphs.
The Inverse Trigonometric Functions.
Right Triangle Trigonometry.
6. Trigonometric Identities and Conditional Equations.
Basic Identities.
Verifying Identities.
Sum and Difference Identities.
Double-Angle and Half-Angle Identities.
Product and Sum Identities.
Conditional Trigonometric Equations.
7. Applications of Trigonometry.
The Law of Sines.
The Law of Cosines.
Vectors.
Trigonometric Form of Complex Numbers.
Powers and Roots of Complex Numbers.
Polar Equations.
Parametric Equations.
8. Systems of Equations and Inequalities.
Systems of Linear Equations in Two Variables.
Systems of Linear Equations in Three Variables.
Nonlinear Systems of Equations.
Partial Fractions. Inequalities and Systems of Inequalities in Two Variables. The Linear Programming Model.
9. Matrices and Determinants.
Solving Linear Systems Using Matrices.
Operations with Matrices.
Multiplication of Matrices.
Inverses of Matrices.
Solution of Linear Systems in Two Variables Using Determinants.
Solution of Linear Systems in Three Variables Using Determinants.
10. The Conic Sections.
The Parabola.
The Ellipse and the Circle.
The Hyperbola.
Rotation of Axes.
Polar Equations of the Conics.
11. Sequences, Series, and Probability.
Sequences.
Series.
Geometric Sequences and Series.
Counting and Permutations.
Combinations, Labeling, and the Binomial Theorem.
Probability.
Mathematical Induction.
Appendix: Basic Algebra Review.
Real Numbers and Their Properties.
Exponents and Radicals.
Polynomials.
Factoring Polynomials.
Rational Expressions.