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Comprehensive Study Guide: College Algebra Foundations and Key Topics

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Linear Equations

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

Intro to Functions & Their Graphs

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

Function Operations

  • Adding & Subtracting Functions
    5:56
  • Adding & Subtracting Functions Example 1
    4:46
  • Multiplying & Dividing Functions
    7:24

Quadratic Functions

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

Understanding Polynomial Functions

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

Zeros of Polynomial Functions

    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

    Introduction to Exponential Functions

    • Exponential Functions
      6:13

    The Number e

    • The Number e
      4:47

    Introduction to Logarithms

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

    Properties of Logarithms

    • Change of Base Property
      5:36
    • Product, Quotient, and Power Rules of Logs
      3:49
    • Expand & Condense Log Expressions
      4:22

    Solving Exponential and Logarithmic Equations

    • Solving Exponential Equations Using Logs
      5:47
    • Solving Exponential Equations Using Like Bases
      4:46
    • Solving Logarithmic Equations
      5:02

    Two Variable Systems of Linear Equations

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

    Introduction to Matrices

    • Performing Row Operations on Matrices
      8:38
    • Example 1
      13:06
    • Solving Systems of Equations - Matrices (Reduced Row-Echelon Form)
      5:58

    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

    Circles

    • Circles in Standard Form
      5:18
    • Circles in General Form
      6:20
    • Circles in Standard Form Example 1
      3:40

    Parabolas

    • Parabolas as Conic Sections Example 1
      7:12
    • Horizontal Parabolas
      5:28
    • Horizontal Parabolas Example 1
      7:18

    Ellipses: Standard Form

    • Graph Ellipses NOT at Origin
      4:50
    • Foci and Vertices of an Ellipse
      5:30
    • Graph Ellipses at Origin
      5:12

    Hyperbolas at the Origin

    • Asymptotes of Hyperbolas
      5:50
    • Graphing Hyperbolas at the Origin Example 1
      3:58
    • Introduction to Hyperbolas
      6:15