Study well.

## Precalculus

#### Preliminaries:

Interval and Set NotationIntercepts

#### Part 1 - An Introduction to Functions

Relations

What is a Function?

Functions: A Graphical View

Function Notation

1.2 - More With Functions

Six Basic Functions

Operations on Functions

What is a Zero of a Function?

Symmetry

Even and Odd Functions

1.3 - Graphs of Functions

Piecewise Functions

Increasing, Decreasing, and Constant

Absolute and Local Extrema

1.4 - Translations of Graphs

Horizontal and Vertical Translations

Reflecting Graphs

Vertically Stretching and Shrinking Graphs

1.5 - Linear Functions

Slope

Horizontal and Vertical Lines

Slope-Intercept Form of a Line

Point-Slope Form of a Line

Finding Equations of Lines

#### Part 2 - Polynomial, Rational, and Radical Functions

Quadratic Functions

The Vertex Formula

The Quadratic Formula

The Discrminant

2.2 Reading Graphs, Absolute Value Equations and Inequalities, and Quadratic Inequalities

Reading Graphs to Determine the Solutions of Equations and Inequalities

Absolute Value Equations and Inequalities - Part 1

Absolute Value Equations and Inequalities - Part 2

Quadratic Inequalities

2.3 - Introduction to Polynomial Functions

Definition of a Polynomial Function

End Behavior of a Polynomial Function

Recall - What is a Zero of a Function?

Repeated Zeros

2.4 - The Remainder and Factor Theorems

Synthetic Division

The Remainder and Factor Theorems

2.5 - Zeros of Polynomial Functions

Complex Zeros

Finding the Zeros of a Polynomial Function

2.6 - Rational Functions

Rational Functions

Asymptotes of Rational Functions

Graphing Rational Functions

2.7 - Rational Equations and Inequalitites

Rational Equations

Rational Inequalities

2.8 - Radical Equations and Inequalities

Radical Functions

Radical Equations

#### Part 3 - Exponential and Logarithmic Functions

Composition of Functions

One-to-One Functions

Inverse Functions

3.2 - Exponential and Logarithmic Functions

Exponential Functions

Definition of Logarithm

Properties of Logarithms

Change of Base Formula

Logarithmic Functions

3.3 - Exponential and Logarithmic Equations

Exponential Equations

Logarithmic Equations

Compound Interest

Exponential Growth and Decay

Million, Billion, Trillion

#### Part 4 - Matrices

The General Idea of a Matrix

Matrices - Row Operations - Part 1

Matrices - Row Operations - Part 2

Matrices - Row Operations - Part 3

Matrices - Row Operations - Part 4

4.2 - Properties of Matrices

Properties of Matrices

Matrix Multiplication

Determinants

Inverse of a 2x2 Matrix

4.3 - Partial Fractions

Partial Fractions - Part 1

Partial Fractions - Part 2

**Part 5 - Conic Sections**

5.1 - Circles

Circles - Part 1

Circles - Part 2

5.2 - Parabolas

Parabolas - Part 1

Parabolas - Part 2

Parabolas - Part 3

Parabolas - Part 4

5.3 - Ellipses

Ellipses - Part 1

Ellipses - Part 2

5.4 - Hyperbolas

Hyperbolas - Part 1

Hyperbolas - Part 2

Hyperbolas - Part 3

5.5 - The General Equation of Conic Sections and Eccentricity

The General Equation of Conic Sections and Eccentricity

**Part 6 - The Foundations of Trigonometry**

6.1 - Angles, Radians, and Arc Length

Angles

Radians

Arc Length

6.2 - Definition of Trigonometric Functions and Fundamental Identities

Definition of Trigonometric Functions

Fundamental Trigonometric Identities

6.3 - Right Triangle Trigonometry

The Definition of Trigonometric Functions for Right Triangles

Trigonometric Function Values of Special Angles

Reference Angles

6.4 - Graphs of Sine and Cosine Functions

An Introduction to Graphing to Sine and Cosine

Graphs of Sine and Cosine - Part 1

Graphs of Sine and Cosine - Part 2

Graphs of Sine and Cosine - Part 3

6.5 - Verifying Trigonometric Identities

Verifying Trigonometric Identities

6.6 - More Trigonometric Identities

Derivation of Sum and Difference Identities for Cosine and Sine

Sum and Difference Identities

Double Angle Identities

Half-Angle Identities

6.7 - Inverse Trigonometric Functions

Inverse Trigonometric Functions

6.8 - Trigonometric Equations

Trigonometric Equations - Part 1

Trigonometric Equations - Part 2

**Part 7 - Applications of Trigonometry**

7.1 - The Law of Sines and The Law of Cosines

The Law of Sines - Part 1

The Law of Sines - Part 2

The Law of Cosines

7.2 - An Introduction to Vectors

An Introduction to Vectors - Part 1

An Introduction to Vectors - Part 2

An Introduction to Vectors - Part 3

7.3 - The Polar (Trigonometric) Form of Complex Numbers

The Polar Form of Complex Numbers

Powers and Roots of Complex Numbers

7.4 - Polar Equations

Polar Equations

Graphing Polar Equations

7.5 - An Introduction to Parametric Equations

An Introduction to Parametric Equations