Precalculus

<h2>Table of Contents</h2> <div class="c-non-traditional-number-list_container"> <ol> <li><strong>Graphs, Functions, and Models</strong> <ul> <li>1.1 Introduction to Graphing</li> <li>1.2 Functions and Graphs</li> <li>1.3 Linear Functions, Slope, and Applications</li> <li>1.4 Equations of Lines and Modeling</li> <li>1.5 Linear Equations, Functions, Zeros, and Applications</li> <li>1.6 Solving Linear Inequalities</li> </ul> </li> <li><strong>More on Functions</strong> <ul> <li>2.1 Increasing, Decreasing, and Piecewise Functions; Applications</li> <li>2.2 The Algebra of Functions</li> <li>2.3 The Composition of Functions</li> <li>2.4 Symmetry</li> <li>2.5 Transformations</li> <li>2.6 Variation and Applications</li> </ul> </li> <li><strong>Quadratic Functions and Equations; Inequalities</strong> <ul> <li>3.1 The Complex Numbers</li> <li>3.2 Quadratic Equations, Functions, Zeros, and Models</li> <li>3.3 Analyzing Graphs of Quadratic Functions</li> <li>3.4 Solving Rational Equations and Radical Equations</li> <li>3.5 Solving Equations and Inequalities with Absolute Value</li> </ul></li> <li><strong>Polynomial Functions and Rational Functions</strong> <ul> <li>4.1 Polynomial Functions and Models</li> <li>4.2 Graphing Polynomial Functions</li> <li>4.3 Polynomial Division; The Remainder Theorem and the Factor Theorem</li> <li>4.4 Theorems about Zeros of Polynomial Functions</li> <li>4.5 Rational Functions</li> <li>4.6 Polynomial Inequalities and Rational Inequalities</li> </ul></li> <li><strong>Exponential Functions and Logarithmic Functions</strong> <ul> <li>5.1 Inverse Functions</li> <li>5.2 Exponential Functions and Graphs</li> <li>5.3 Logarithmic Functions and Graphs</li> <li>5.4 Properties of Logarithmic Functions</li> <li>5.5 Solving Exponential Equations and Logarithmic Equations</li> <li>5.6 Applications and Models: Growth and Decay; Compound Interest</li> </ul></li> <li><strong>The Trigonometric Functions</strong> <ul> <li>6.1 Trigonometric Functions of Acute Angles</li> <li>6.2 Applications of Right Triangles</li> <li>6.3 Trigonometric Functions of Any Angle</li> <li>6.4 Radians, Arc Length, and Angular Speed</li> <li>6.5 Circular Functions: Graphs and Properties</li> <li>6.6 Graphs of Transformed Sine and Cosine Functions</li> </ul></li> <li><strong>Trigonometric Identities, Inverse Functions, and Equations</strong> <ul> <li>7.1 Identities: Pythagorean and Sum and Difference</li> <li>7.2 Identities: Cofunction, Double-Angle, and Half-Angle</li> <li>7.3 Proving Trigonometric Identities</li> <li>7.4 Inverses of the Trigonometric Functions</li> <li>7.5 Solving Trigonometric Equations</li> </ul></li> <li><strong>Applications of Trigonometry</strong> <ul> <li>8.1 The Law of Sines</li> <li>8.2 The Law of Cosines</li> <li>8.3 Complex Numbers: Trigonometric Notation</li> <li>8.4 Polar Coordinates and Graphs</li> <li>8.5 Vectors and Applications</li> <li>8.6 Vector Operations</li> </ul></li> <li><strong>Systems of Equations and Matrices</strong> <ul> <li>9.1 Systems of Equations in Two Variables</li> <li>9.2 Systems of Equations in Three Variables</li> <li>9.3 Matrices and Systems of Equations</li> <li>9.4 Matrix Operations</li> <li>9.5 Inverses of Matrices</li> <li>9.6 Determinants and Cramer’s Rule</li> <li>9.7 Systems of Inequalities and Linear Programming</li> <li>9.8 Partial Fractions</li> </ul></li> <li><strong>Conic Sections</strong> <ul> <li>10.1 The Parabola</li> <li>10.2 The Circle and the Ellipse</li> <li>10.3 The Hyperbola</li> <li>10.4 Nonlinear Systems of Equations and Inequalities</li> <li>10.5 Rotation of Axes</li> <li>10.6 Polar Equations of Conics</li> <li>10.7 Parametric Equations</li> </ul></li> <li><strong>Sequences, Series, and Combinatorics</strong> <ul> <li>11.1 Sequences and Series</li> <li>11.2 Arithmetic Sequences and Series</li> <li>11.3 Geometric Sequences and Series</li> <li>11.4 Mathematical Induction</li> <li>11.5 Combinatorics: Permutations</li> <li>11.6 Combinatorics: Combinations</li> <li>11.7 The Binomial Theorem</li> <li>11.8 Probability</li> </ul> </li> </ol> </div>