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College Algebra Study Guide: Fundamental Concepts, Equations, Functions, and Applications

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Exponents

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

Radical Expressions

  • Square Roots
    05:49
  • Nth Roots
    06:56

Rational Exponents

  • Rational Exponents
    04:06

Polynomials Intro

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

Factoring Polynomials

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

Rational Equations

  • Introduction to Rational Equations
    05:56
  • Restrictions on Rational Equations
    05:21

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

Complex Numbers

  • Dividing Complex Numbers
    04:22
  • Introduction to Complex Numbers
    03:31
  • Adding and Subtracting Complex Numbers
    03:18

The Square Root Property

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

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

Intro to Functions & Their Graphs

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

Transformations

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

Function Composition

  • Evaluating Composed Functions
    4:26
  • Decomposition of Functions Example 1
    1:46
  • Domain Restrictions of Composed Functions
    3:51

Circles

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

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

    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

    Introduction to Exponential Functions

    • Exponential Functions
      6:13

    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