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Comprehensive Study Notes: Functions, Limits, Differentiation, and Integration for College Algebra & Calculus

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Intro to Functions & Their Graphs

  • Finding the Domain of an Equation
    3:43
  • Relations & Functions Example 1
    1:30
  • Relations and Functions
    5:20

Common Functions

  • Graphs of Common Functions
    5:57

Transformations

  • Stretches & Shrinks of Functions
    6:02
  • Shifts of Functions
    5:34
  • Domain & Range of Transformed Functions
    4:22

Exponents

  • Simplifying Exponential Expressions
    6:39
  • Introduction to Exponent Rules
    7:39
  • Zero and Negative Rules
    6:37

Introduction to Exponential Functions

  • Exponential Functions
    6:13

Introduction to Logarithms

  • Evaluate Logarithms
    5:14
  • Logarithms Introduction
    7:30
  • The Natural Log
    2:51

Graphs and Coordinates

  • Graphs and Coordinates - Example
    02:16
  • Graphs & the Rectangular Coordinate System
    05:10

Linear Equations

  • Solving Linear Equations with Fractions
    04:02
  • Introduction to Solving Linear Equtions
    07:48
  • Categorizing Linear Equations
    06:00

The Square Root Property

  • Imaginary Roots with the Square Root Property
    02:20
  • Solving Quadratic Equations by the Square Root Property
    06:12

Intro to Quadratic Equations

  • Introduction to Quadratic Equations
    05:35
  • Solving Quadratic Equations by Factoring
    06:08

Completing the Square

  • Solving Quadratic Equations by Completing the Square
    06:24

The Quadratic Formula

  • Solving Quadratic Equations Using The Quadratic Formula
    06:36
  • The Discriminant
    04:11

Choosing a Method to Solve Quadratics

  • Choosing a Method to Solve Quadratics
    04:03

Quadratic Functions

  • Converting Standard Form to Vertex Form
    04:34
  • Vertex Form
    08:07
  • Example 2
    7:49

Algebraic Expressions

  • Evaluating Algebraic Expressions
    03:11
  • Introduction to Algebraic Expressions
    05:09
  • Introduction to College Algebra Channel
    1:51

Polynomials Intro

  • Standard Form of Polynomials
    05:16
  • Introduction to Polynomials
    05:13
  • Adding and Subtracting Polynomials
    03:34

Multiplying Polynomials

  • Special Products - Cube Formulas
    03:41
  • Special Products - Square Formulas
    04:14
  • FOIL
    03:07

Factoring Polynomials

  • Factor Using the AC Method When a Is 1
    4:16
  • Factor by Grouping
    04:36
  • Introduction to Factoring Polynomials
    07:30

Understanding Polynomial Functions

  • Introduction to Polynomial Functions
    06:04
  • Maximum Turning Points of a Polynomial Function
    02:44
  • Finding Zeros & Their Multiplicity
    03:42

Graphing Polynomial Functions

  • Example 1
    09:43
  • Identifying Intervals of Unknown Behavior
    05:01
  • Graphing Polynomial Functions
    05:25

Zeros of Polynomial Functions

    Linear Inequalities

    • Interval Notation
      05:18
    • Linear Inequalities with Fractions & Variables on Both Sides
      03:42
    • Linear Inequalities
      06:07

    Two-Variable Equations

    • Graphing Equations of Two Variables by Plotting Points
      04:29
    • Graphing Intercepts
      04:08
    • Equations with Two Variables
      05:28

    Two Variable Systems of Linear Equations

    • Example 1
      3:09
    • Solving Systems of Equations - Elimination
      6:48
    • Example 2
      3:31

    Introduction to Rational Functions

    • Intro to Rational Functions
      6:04

    Asymptotes

    • Introduction to Asymptotes
      6:24
    • Determining Horizontal Asymptotes
      4:48
    • Determining Removable Discontinuities (Holes)
      3:34

    Graphing Rational Functions

    • Graphing Rational Functions Using Transformations
      5:31
    • Example 1
      3:08
    • Example 1
      10:18

    Sequences

    • Example 2
      4:19
    • Example 1
      5:52
    • Introduction to Sequences
      8:22

    Arithmetic Sequences

    • Example 2
      7:00
    • Example 1
      2:35
    • Arithmetic Sequences - Recursive Formula
      6:40

    Geometric Sequences

    • Geometric Sequences - General Formula
      4:45
    • Geometric Sequences - Recursive Formula
      4:18