Precalculus Algebra

Mathematical Modeling
 
Goals of this Section
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Terminology To Know
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What is mathematical reasoning?
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Logical Deduction
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Types of Information
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Is this actually math?
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Math as a Language
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Types of Numbers
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Numeric Model Walkthrough
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Embrace Laziness!
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Variables and Their Roles
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Generalized Model Walkthrough
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Variables, Functions, Graphing, and Universal Properties
 
Goals of this Section
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Terminology To Know
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Relationship vs. Equations
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Relationship vs. Functions
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Functions Require Context
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Domain, Codomain, and Range
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Set Notation
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Function Notation
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f(x) Notation
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Function Composition
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Graphing Introduction
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Terminology To Know
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French History and Dinosaurs!
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Graphing To Relate Variables
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Graphs Aren’t Precise
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Using Graphs
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Vertical Line Test
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Library Of Functions
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Parent Functions
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Parent Functions
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Universal Properties
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Terminology To Know
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Geometric Vs Analytic Viewpoints
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Geometric Perspective
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Analytic Viewpoint
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Even Functions
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Odd Functions
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Intro: Rigid Translations
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Rigid Translations: Geometrics
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Rigid Translation Practice
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Rigid Translations: Analytics
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Rigid Translation Practice
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Transforms: Geometric
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Transforms: Analytic
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Transform Practice
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Transform And Translates
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Rigid Translation and Transformations Practice
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Points of Interest on Graphs - Zeros
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Sign Charts
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Points of Interest on Graphs - Extrema
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POI-Extrema Practice
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Continuity
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Points of Interest on Graphs - Discontinuities
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POI-Discontinuities Practice
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Algebra with Functions
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Equals Signs are Magic!
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One and Zero; the Most Useful of Numbers
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Inverse Functions
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Horizontal Line Test
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HLT Practice
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Inverse Function - Analytic View
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Invertible Function Practice
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Exploration of Functions
 
Polynomial Functions
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Terminology To Know
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What is (and isn’t) a Polynomial?
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Fundamental Theorem of Algebra
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An Interjection into Polynomial History!
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Exponents and Extrema: An Example
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Exponents and Extrema 2: Local Extrema
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Curvature and Graphing
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Factoring: Introduction
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Factoring: Common Factors
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Factoring: Round One!
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Factoring; Grouping Method
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Factoring; AC Method
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Factoring; Special Forms
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Completing the Square
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Polynomial Long Division
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Polynomial Synthetic Division
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Rational Root Theorem
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Complex Numbers
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Simplifying Complex Numbers
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Quadratic Formula
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Comprehensive Factoring Quiz
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Radical Functions
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Terminology To Know
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Why Radicals?
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Simplifying Radicals - Part 1
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Simplifying Radicals - Part 2
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Square Root: the Inverse Function
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Solving Unsimplified Radicals
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Inequalities
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Terminology To Know
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What are Inequalities?
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Computing inequalities
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Computing Inequalities Practice
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Algebra with Inequalities
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Solving Inequalities
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Solving Inequalities Practice
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Graphing Inequalities
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Exponential Functions: Goals
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Terminology To Know
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A Review of Exponential Functions
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Simplifying Numeric Exponentials
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Properties of Exponentials
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Unlimited Practice for Properties of Exponentials
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Practice Solving Exponential Equations 2
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Properties of the Exponential Function
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Practice Solving Exponential Equations 1
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Exponential Growth and Decay
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Simplifying Numeric Exponentials
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Logarithmic Functions
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Terminology To Know
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Introduction and Notation of Logarithms
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Practice with Simplifying Numeric Logarithms
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Logs as Inverse Functions
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Properties Of Logs
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Practice with Properties of Logarithms: Expansion
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Common Mistakes Of Logs
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Change of Base formula
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Practice with change of base
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Examples of Logs
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Practice with Solving Logarithmic Equations
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Piecewise Functions
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Piecewise Functions: The Geometric View
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Piecewise Functions: The Analytic View
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Piecewise: Analytic View Practice 1
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Domains of Piecewise Functions
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Identify Piecewise Discontinuities
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Piecewise Functions: Computation
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Piecewise: Computation Practice 1
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Absolute Value Functions
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Absolute Value: Geometric View
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Modeling Distance Practice 1
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Absolute Value: Analytic View
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Absolute Value: Analytic View Practice 1
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Computing Absolute Values
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Compute Absolute Value Practice 1
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Graphing Absolute Values
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Absolute Value: Solving Equalities
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Compute Absolute Value Practice 1
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Rational Functions
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Terminology To Know
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What is a rational function?
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Domain of rational functions
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Rational Function Domains Practice 1
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Vertical Asymptotes
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Holes in Domains of Rational Functions
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Rational Function Discontinuities Practice 1
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Horizontal Asymptotes
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Rational Function Horizontal Asymptote Practice 1
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Overall
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