About This Chapter
Standard: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). (CCSS.Math.Content.HSF-IF.A.1)
Standard: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. (CCSS.Math.Content.HSF-IF.A.2)
Standard: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n greater than or equal to 1. (CCSS.Math.Content.HSF-IF.A.3)
About This Chapter
With a thorough understanding of functions, students are able to recognize the range and domain inside of a function, evaluate different functions, compare functions and compare explicit functions as well. Students who comprehend the fundamentals of functions will also be able to solve application problems with functions and be familiar with graphing inverse functions.
The lessons in this standard also cover the following topics:
- Calculating functions from a context
- Application problems using functions
- Adding, subtracting, multiplying and dividing functions
- Composing functions
- Inverse functions
- Verifying and finding inverse functions
- Finding the inverses of functions represented by tables or graphs
- Producing an invertible function from a non-invertible function by restricting the domain
- Applying function problems
You'll know that students have mastered this standard once they've shown that they understand how to solve simple functions, how to calculate functions with an inverse and how to write expressions. They'd also comprehend the relationship of domain to range and identify elements of both. The lessons and the standard can prepare your students for college-level math and careers such as those in engineering, business data analysis and bookkeeping.
How to Use These Lessons in Your Classroom
Below are a few tips for incorporating these lessons on functions into your regular curriculum in order to help meet the common core standards.
Review and Preview Lessons
At the beginning of class, show a few minutes of the previous lesson's video that reviews the most important parts of the lesson as a way to refresh students' memories. Point out vital parts of the lesson. You can also give them a brief preview of the current lesson so they have an idea of what to expect and so they can prepare themselves to absorb the lesson.
Watch the short video lesson on the basics of functions. Have students take the quiz associated with the lesson to see how well they understand the concepts. After teaching the lesson from your curriculum and discussing functions in class, have them re-take the quiz to assess further comprehension.
When you reach the 'Add, Subtract, Multiply and Divide Functions' lesson, you can use flashcards in order to help students learn better. Flashcards are effective because they give students visual learning aids that can help with recall during testing. Unlike memorizing information from a textbook, the varied order of flashcards helps students learn, understand and retain the concepts.
1. Functions: Identification, Notation & Practice Problems
A function is simply a rule that takes one number and turns it into another. But some special conditions must apply for it to be a true mathematical function. Learn about those conditions and how we write functions here!
2. What Is Domain and Range in a Function?
The domain and range are the possible outputs and inputs of a function. In this lesson, learn about what might restrict the domain and how to figure out the domain and range from a graph.
3. 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!
4. 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.
5. 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.
6. 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.
7. 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!
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Other chapters within the Common Core Math - Functions: High School Standards course
- Common Core HS Functions - Sequences
- Common Core HS Functions - Graphing
- Common Core HS Functions - Linear Functions
- Common Core HS Functions - Quadratic Functions
- Common Core HS Functions - Common Functions & Transformations
- Common Core HS Functions - Polynomial Functions
- Common Core HS Functions - Rational Functions
- Common Core HS Functions - Exponential & Logarithmic Functions
- Common Core HS Functions - Trigonometric Functions