About This Chapter
Standard: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. (CCSS.Math.Content.HSF-IF.C.7b)
Standard: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x),f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. (CCSS.Math.Content.HSF-BF.B.3)
About This Chapter
With a thorough knowledge of common functions and transformations, students will be able to graph square root and cube root functions in addition to being able to recognize piecewise functions. Students will also have the ability to use technology as a way to explain graph effects.
The lesson topics for this standard include:
- How to graph piecewise functions
- Graph step functions
- Graph absolute value functions
- Shifting, reflecting, stretching and compressing shapes
You'll be able to recognize when students have a grasp on the standard when they can adequately explain such function transformations as reflecting, shifting, stretching and compressing. The information students learn could prove useful in preparing them for college and a future career in such industries as construction and masonry, art, architecture and engineering.
How to Use These Lessons in Your Classroom
Below are suggestions that you could include in your regular curriculum to help you meet Common Core standards.
Create a Graphing and Transformation Game
Create a game that your students can play to make learning more enjoyable. Have them identify basic shapes within the classroom, then write functional equations that allow them to graph the object. Then have them use reflection, stretching or compression to transform the shape on the graph.
Finding the Matches
Watch the lessons on graphing piecewise, step and absolute value functions. Draw different graphs representing these functions on one side of the blackboard and equations for the graphs on the other side. Have the students match the graphs to the equations.
Use Quizzes as Pre-Tests
If you find that you don't have the time to preview upcoming lessons, you can instead use the quizzes as no-credit pre-tests before teaching the actual lesson. Once students have learned about graphing functions and transformations, have them re-take the quiz to show them how much they've learned.
1. What are Piecewise Functions?
A piecewise function is a certain type of function that is made up of different parts. This lesson will define and describe piecewise functions and teach you how to identify them and how to write them.
2. How to Graph Piecewise Functions
Piecewise functions are specific functions that have more than one piece. There is a special trick to graphing these type of functions, which you will learn in this lesson.
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Other chapters within the Common Core Math - Functions: High School Standards course
- Common Core HS Functions - Basics
- 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 - Polynomial Functions
- Common Core HS Functions - Rational Functions
- Common Core HS Functions - Exponential & Logarithmic Functions
- Common Core HS Functions - Trigonometric Functions