# Ch 1: Common Core HS Functions - Basics

Let us help you to teach your high school students about the basics of functions in accordance with the Common Core State Standards. Get tips on how to use lessons in the classroom and how to know when your students have mastered the standard.

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)

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.

#### Pre-Quiz Students

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.

#### Make Flashcards

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.

7 Lessons in Chapter 1: Common Core HS Functions - Basics
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Chapter Practice Exam
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Practice Final Exam
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### Other Chapters

Other chapters within the Common Core Math - Functions: High School Standards course

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