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Math Tutorial 16.5 - Piecewise Functions

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There are 6 lessons in this math tutorial covering Piecewise Functions. The tutorial starts with an introduction to Piecewise Functions and is then followed with a list of the separate lessons, the tutorial is designed to be read in order but you can skip to a specific lesson or return to recover a specific math lesson as required to build your math knowledge of Piecewise Functions. you can access all the lessons from this tutorial below.

In this Math tutorial, you will learn:

  • What are piecewise functions? Why are they called so?
  • What are the limit points for piecewise functions?
  • How to find the domain and range of piecewise functions?
  • What is a continuous function?
  • How to check the continuity of a piecewise function?
  • How to plot the graph of a piecewise function?
  • How to know whether a piecewise function is continuous or not without plotting the graph?
  • How to deal with piecewise functions with more than two parts?
  • How to deal with piecewise functions with any constant piece?
  • What is the absolute value function?
  • How absolute value functions are related to piecewise functions?
  • How to plot the graph of an absolute value function?

Introduction

So far, we have dealt with examples where the functions are made up of a single equation in the entire domain. As a result, those functions give the same type of line as a representing graph. This occurs not only in simple functions but also in composite functions too. This is because a combined function integrates all functions it contains in the entire domain.

In this tutorial instead, we will consider some special functions where the formula is different in different parts of the domain. Thus, in a certain sense, we are going to deal with composite functions connected in series (the combination takes place one after another), not in parallel (the combination takes place at the same time throughout the entire domain). Such functions are known as "piecewise", i.e. "one piece at a time".

Please select a specific "Piecewise Functions" lesson from the table below, review the video tutorial, print the revision notes or use the practice question to improve your knowledge of this math topic.

Functions Learning Material
Tutorial IDMath Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
16.5Piecewise Functions
Lesson IDMath Lesson TitleLessonVideo
Lesson
16.5.1The Meaning of Piecewise Functions
16.5.2Domain and Range of Piecewise Defined Functions
16.5.3Continuity of a Piecewise Function
16.5.4Piecewise Functions with More than Two Parts
16.5.5Piecewise Functions with Constant Pieces
16.5.6Absolute Value Function as a Special Case of Piecewise Functions

Whats next?

Enjoy the "Piecewise Functions" math tutorial? People who liked the "Piecewise Functions" tutorial found the following resources useful:

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  2. Functions Revision Notes: Piecewise Functions. Print the notes so you can revise the key points covered in the math tutorial for Piecewise Functions
  3. Functions Practice Questions: Piecewise Functions. Test and improve your knowledge of Piecewise Functions with example questins and answers
  4. Check your calculations for Functions questions with our excellent Functions calculators which contain full equations and calculations clearly displayed line by line. See the Functions Calculators by iCalculator™ below.
  5. Continuing learning functions - read our next math tutorial: Inverse Functions

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