Graphical Approach to Precalculus With Limits

1. Linear Functions, Equations, and Inequalities. Real Numbers and Coordinate Systems. Introduction to Relations and Functions. Linear Functions. Equations of Lines and Linear Models. Linear Equations and Inequalities. Applications of Linear Functions. 2. Analysis of Graphs of Functions. Graphs of Basic Functions and Relations; Symmetry. Vertical and Horizontal Shifts of Graphs. Stretching, Shrinking, and Reflecting Graphs. Absolute Value Functions: Graphs, Equations, Inequalities, and Applications. Piecewise-Defined Functions. Operations and Composition. 3. Polynomial Functions. Complex Numbers. Quadratic Functions and Graphs. Quadratic Equations and Inequalities. Further Applications of Quadratic Functions and Models. Higher Degree Polynomial Functions and Graphs. Topics in the Theory of Polynomial Functions (I). Topics in the Theory of Polynomial Functions (II). Polynomial Equations and Inequalities; Further Applications and Models. 4. Rational, Power, and Root Functions. Rational Functions and Graphs. More on Graphs of Rational Functions. Rational Equations, Inequalities, Applications, and Models. Functions Defined by Powers and Roots. Equations, Inequalities, and Applications Involving Root Functions. 5. Inverse, Exponential, and Logarithmic Functions. Inverse Functions. Exponential Functions. Logarithms and Their Properties. Logarithmic Functions. Exponential and Logarithmic Equations and Inequalities. Applications and Modeling with Exponential and Logarithmic Functions. 6. Analytic Geometry. Circles and Parabolas. Ellipses and Hyperbolas. Summary of the Conic Sections. Parametric Equations. 7. Matrices and Systems of Equations and Inequalities. Systems of Equations. Solution of Linear Systems by the Echelon Method. Solution of Linear Systems by Row Transformations. Matrix Properties and Operations. Determinants and Cramer's Rule. Solution of Linear Systems by Matrix Inverses. Systems of Inequalities and Linear Programming. Partial Fractions. 8. Trigonometric Functions and Applications. Angles and Arcs The Unit Circle Graphs of the Sine and Cosine Functions Graphs of the Other Circular Functions Functions of Angles and Fundamental Identities Evaluating Trigonometry Functions Applications of Right Triangles Harmonic Motion 9. Trigonometric Identities and Equations. Identities. Further Identities. The Inverse Circular Functions. Trigonometric Equations and Inequalities. Further Equations and Inequalities. 10. Applications of Trigonometry; Vectors. The Law of Sines. The Law of Cosines and Area Formulas. Vectors and Their Applications. [read more]