About This Chapter
Below is a sample breakdown of the Function Operations chapter into a 5-day school week. Based on the pace of your course, you may need to adapt the lesson plan to fit your needs.
|Day||Topics||Key Terms and Concepts Covered|
|Monday||How to Add, Subtract, Multiply and Divide Functions||Methods of performing basic operations with functions|
|Tuesday||How to Compose Functions; Applying Function Operations Practice Problems|| The process of writing equations and combining functions;|
Practical experience with function operations
|Wednesday|| Compounding Functions and Graphing Functions of Functions;|
Domain and Range of Composite Functions: Definition and Examples
|The methods of compounding and graphing functions;|
How one function's domain and range influences another's
|Thursday|| Inverse Functions;|
Understanding and Graphing the Inverse Function
|Techniques for writing, finding and graphing inverse functions|
|Friday|| One-to-One Functions: Definitions and Examples;|
Manipulating Functions and Solving Equations for Different Variables
| The algebraic definition of one-to-one functions;|
How to solve equations for different variables
1. How to Add, Subtract, Multiply and Divide Functions
Adding, subtracting, multiplying and dividing functions is about as simple as substituting in expressions and then just doing whichever operation it asks you to do. Check out this video lesson to see some examples of this and learn just how easy it is!
2. How to Compose Functions
Function composition is the process of putting two or more functions together. This video lesson will explain how this process works and also show you how to evaluate functions that have been composed.
3. Applying Function Operations Practice Problems
In this lesson, learn how to apply all the different properties of functions to solve complex problems. From function operations and composition to domain and range, get your practice here!
4. Compounding Functions and Graphing Functions of Functions
We know that functions map numbers to other numbers, so what happens when you have a function of a function? Welcome to functions within functions, the realm of composite functions!
5. Domain & Range of Composite Functions: Definition & Examples
Learn what makes a function a composite function and also learn how the parts of a composite function determine its domain. Also in this video lesson, learn about the range of composite functions.
6. Inverse Functions
Inverse functions are two functions that do exactly opposite things. Check out this lesson to learn about how to write inverse functions, find inverse functions, and predict whether or not they exist.
7. Understanding and Graphing the Inverse Function
If you use a function to map a to b, is there a way to go back from b to a again? Learn how to find and graph inverse functions so that you can turn a into b and back into a.
8. One-to-One Functions: Definitions and Examples
Watch this video lesson to learn what makes a one-to-one function different from a regular function. Learn a simple test you can use to check whether a function is one-to-one or not.
9. Manipulating Functions and Solving Equations for Different Variables
Functions can be manipulated to solve for many different variables. There are certain rules to follow, but if the rules are adhered to, solving equations can be quite simple. This lesson will show you how.
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