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College Algebra Study Guide: Graphs, Functions, and Linear Models

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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

Graphs and Coordinates

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

Lines

  • Point-Slope Form
    05:46
  • Graphing Lines in Slope-Intercept Form
    02:35
  • Types of Slope
    05:17

Linear Equations

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

Linear Inequalities

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

Function Operations

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

Complex Numbers

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

Intro to Quadratic Equations

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

Quadratic Functions

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

The Square Root Property

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

Function Composition

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

Transformations

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

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

Dividing Polynomials

    Zeros of Polynomial Functions

      Rational Equations

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

      Introduction to Rational Functions

      • Intro to Rational Functions
        6:04

      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

      Graphing Exponential Functions

      • Transformations of Exponential Graphs Example 1
        4:12
      • Graphing Exponential Functions Example 1
        3:58
      • Transformations of Exponential Graphs
        6:16

      The Number e

      • The Number e
        4:47

      Introduction to Logarithms

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

      Graphing Logarithmic Functions

      • Graphing Logarithmic Functions
        4:30
      • Transformations of Logarithmic Graphs
        4:37
      • Graphs of Logarithmic Functions
        5:26

      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