Section 1.4 Topics Covered in MTH 111
¶Explanations, Examples, and Exercises.
Please note that the documents open in new windows.
- Advanced Function Notation
- Difference Quotients
- Even Functions and Odd Functions
- Function Composition
- Inverse Functions
- Graphical Transformations
- Exponential Functions and their Graphs
- Logarithmic Functions and their Graphs
- Interpreting Logarithms as Exponents
- Derivation of the Properties of Logarithms
- Application of the Properties of Logarithms
- Exponential Equations
- Logarithmic Equations
- The Number e and Compound Interest
- Exponential Growth and Decay
- Rational Functions and their Graphs
GeoGebra Applets.
Please note that the Applets open in new windows.
Simplifying \(f(x+y)\) for a quadratic expression \(f\text{.}\) (Exploration and Drill Applet)
Graphical transformations - horizontal shifts. (Exploration Applet)
Graphical transformations - vertical shifts. (Exploration Applet)
Graphical transformations - horizontal and vertical shifts. (Drill Applet)
Graphical transformations - reflections across the axes. (Exploration Applet)
Graphical transformations - horizontal stretches and compressions. (Exploration Applet)
Graphical transformations - vertical stretches and compressions. (Exploration Applet)
Graphical transformations - stretches/compressions/reflections. (Drill Applet)
Graphical transformations - \(g(x)=a \cdot f(b(x - h)) + k\text{.}\) (Drill Applet)
Graphical transformations - \(g(x)=a \cdot f(b x - h) + k\text{.}\) (Drill Applet)
Videos Created by Ann Cary.
The links take you to YouTube Playlists which will open either in a new window or in a Youtube App.
- Algebraically Finding the Domain of a Function (Radical Example)
- Algebraically Finding the Domain of a Function (Rational Example)
- Algebraically Finding the Domain of a Function (Composite Example)
- Evaluating Expressions Using Function Notation
- Finding and Simplifying the Difference Quotient for a Quadratic Function
- Reading the Graph of a Function (Part 1)
- Reading the Graph of a Function (Part 2)
- Algebraically Determining Even/Odd Function (Polynomial Example)
- Algebraically Determining Even/Odd Function (Rational Example)
- Graphical Properties of a Function
- Evaluating a Piecewise-Defined Function
- Graphing a Piecewise-Defined Function
- Find the Formula/Definition for a Piecewise-Defined Function
- Horizontal and Vertical Shift Example
- Vertical Stretch/Compression and Reflection Example
- Horizontal Stretch/Compression and Reflection Example
- Comprehensive Transformation Example
- Composing Functions Represented Numerically (in a Table)
- Composing Functions Represented Graphically
- Composing Functions Algebraically
- Composing Rational Functions Algebraically; Finding the Domain
- Finding the Inverse Function of a Rational Function
- Graphing Inverse Functions and Finding Their Domain and Range
- Composing Rational Functions Algebraically; Finding the Domain
- Determining Zeros, Asymptotes, and Holes of a Rational Function (Example 1)
- Determining Zeros, Asymptotes, and Holes of a Rational Function (Example 2)
- Graphing a Rational Function
- Find the Formula of a Rational Function
- Solving an Exponential Equation (Introduction)
- Finding the Formula for an Exponential Function Given Two Points
- Evaluating Simple Logarithmic Expressions
- Solving a Simple Exponential Equation
- Solving a Simple Logarithmic Equation
- Evaluating Logarithmic Expressions Using Logarithm Properties
- Expanding an Exponential Expression Using Logarithm Properties
- Combining Multiple Logarithmic Expressions Into a Single Logarithm
- Solving an Exponential Equation (Another Example)
- Solving Logarithmic Equation Using the Difference Property of Logarithms
- Solving Logarithmic Equation Using the Sum Property of Logarithms
- Compound Interest Example
- Radioactive Decay Example