MFG College Algebra

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SubsectionCollege Algebra

SubsubsectionChapter 1 Functions and Their Graphs

Functions
Function Notation, Input and Output
- Function Notation, Input and Output
Domain and Range
- Domain and Range
Rates of Change
- Intervals of Increasing and Decreasing
- Rates of Change
Linear Functions
- Linear Functions
Finding Linear Functions
- Finding Linear Functions
Comparing Linear Functions
- Comparing Linear Functions Part 1
- Comparing Linear Functions Part 2

SubsubsectionChapter 2 Modeling with Functions

Piecewise Functions
- Piecewise Functions
Brief Intro to Composite and Inverse Functions
- A Brief Introduction to Composition of Functions
- A Brief Introduction to Inverse Functions

SubsubsectionChapter 3 Exponential Functions

Exponential Functions
- Exponential Functions
Comparing Exponential and Linear Growth
- Comparing Exponential and Linear Growth
- Finding Equations Between Points: Exponential Functions and Linear Functions
Graphs of Exponential Functions
- Graphs of Exponential Functions
Compound Growth
- Compound Growth
- Effective Annual Rates
Continuous Growth
- Continuous Growth

SubsubsectionChapter 4 Logarithmic Functions

Inverse Functions
- Definition and Test
- Finding the Inverse Function
Properties of Logarithms
- Logarithms as Inverse Functions
- Examples
Logarithms and Exponential Models
- Half-Life and Doubling Time
- Logarithms and Exponential Models
Applications of the Logarithm
- Applications of the Logarithm

SubsubsectionChapter 5 Function Transformations

Function Composition
- Function Compositions
Vertical and Horizontal Shifts
- Vertical and Horizontal Shifts
Reflections and Even and Odd Functions
- Reflections
- Even and Odd Functions
Vertical Stretches and Compressions
- Vertical Stretches and Compressions
Horizontal Stretches and Compressions
- Horizontal Stretches and Compressions
Combining Transformations
- Combining Transformations
- Examples of Identifying Function Transformations

SubsubsectionChapter 6 Quadratic Functions

Intro to Quadratic Functions
The Vertex of a Parabola
- The Vertex of a Parabola
- Using Completing the Square to write into Vertix Form

SubsubsectionChapter 7 Power Functions

Combining Functions
- Combining Functions
- Examples of Combining Functions
Power Functions
- Power Functions

SubsubsectionChapter 8 Polynomial and Rational Functions

Polynomial Functions
- Polynomial Functions
- Polynomials Long Run Behavior
Short-Run Behavior
- Short Run Behavior
Long-Run Behavior of Rational Functions
- Rational Functions - Definition and Examples
- Long-Run Behavior of Rational Functions
Short-Run Behavior of Rational Functions
- Short-Run Behavior of Rational Functions