<p><strong>1. Graphs, Functions, and Models</strong><br>1.1 Introduction to Graphing<br>1.2 Functions and Graphs<br>1.3 Linear Functions, Slope, and Applications<br>1.4 Equations of Lines and Modeling<br>1.5 Linear Equations, Functions, Zeros, and Applications<br>1.6 Solving Linear Inequalities<br><strong>2. More on Functions</strong><br>2.1 Increasing, Decreasing, and Piecewise Functions; Applications<br>2.2 The Algebra of Functions<br>2.3 The Composition of Functions<br>2.4 Symmetry<br>2.5 Transformations<br>2.6 Variation and Applications<br><strong>3. Quadratic Functions and Equations; Inequalities</strong><br>3.1 The Complex Numbers<br>3.2 Quadratic Equations, Functions, Zeros, and Models<br>3.3 Analyzing Graphs of Quadratic Functions<br>3.4 Solving Rational Equations and Radical Equations<br>3.5 Solving Equations and Inequalities with Absolute Value<br><strong>4. Polynomial Functions and Rational Functions</strong><br>4.1 Polynomial Functions and Models<br>4.2 Graphing Polynomial Functions<br>4.3 Polynomial Division; The Remainder Theorem and the Factor Theorem<br>4.4 Theorems about Zeros of Polynomial Functions<br>4.5 Rational Functions<br>4.6 Polynomial Inequalities and Rational Inequalities<br><strong>5. Exponential Functions and Logarithmic Functions</strong><br>5.1 Inverse Functions<br>5.2 Exponential Functions and Graphs<br>5.3 Logarithmic Functions and Graphs<br>5.4 Properties of Logarithmic Functions<br>5.5 Solving Exponential Equations and Logarithmic Equations<br>5.6 Applications and Models: Growth and Decay; Compound Interest<br><strong>6. The Trigonometric Functions</strong><br>6.1 Trigonometric Functions of Acute Angles<br>6.2 Applications of Right Triangles<br>6.3 Trigonometric Functions of Any Angle<br>6.4 Radians, Arc Length, and Angular Speed<br>6.5 Circular Functions: Graphs and Properties<br>6.6 Graphs of Transformed Sine and Cosine Functions<br><strong>7. Trigonometric Identities, Inverse Functions, and Equations</strong><br>7.1 Identities: Pythagorean and Sum and Difference<br>7.2 Identities: Cofunction, Double-Angle, and Half-Angle<br>7.3 Proving Trigonometric Identities<br>7.4 Inverses of the Trigonometric Functions<br>7.5 Solving Trigonometric Equations<br><strong>8. Applications of Trigonometry</strong><br>8.1 The Law of Sines<br>8.2 The Law of Cosines<br>8.3 Complex Numbers: Trigonometric Notation<br>8.4 Polar Coordinates and Graphs<br>8.5 Vectors and Applications<br>8.6 Vector Operations<br><strong>9. Systems of Equations and Matrices</strong><br>9.1 Systems of Equations in Two Variables<br>9.2 Systems of Equations in Three Variables<br>9.3 Matrices and Systems of Equations<br>9.4 Matrix Operations<br>9.5 Inverses of Matrices<br>9.6 Determinants and Cramer’s Rule<br>9.7 Systems of Inequalities and Linear Programming<br>9.8 Partial Fractions<br><strong>10. Conic Sections</strong><br>10.1 The Parabola<br>10.2 The Circle and the Ellipse<br>10.3 The Hyperbola<br>10.4 Nonlinear Systems of Equations and Inequalities<br>10.5 Rotation of Axes<br>10.6 Polar Equations of Conics<br>10.7 Parametric Equations<br><strong>11. Sequences, Series, and Combinatorics</strong><br>11.1 Sequences and Series<br>11.2 Arithmetic Sequences and Series<br>11.3 Geometric Sequences and Series<br>11.4 Mathematical Induction<br>11.5 Combinatorics: Permutations<br>11.6 Combinatorics: Combinations<br>11.7 The Binomial Theorem<br>11.8 Probability</p>
