Ch 8: Piecewise and Composite Functions

About This Chapter

How does a piecewise function differ from other functions, such as sine and cosine? Discover what piecewise functions are and why they are important by watching our video lessons.

Piecewise Functions - Chapter Summary and Learning Objectives

Have you worked with piecewise functions? Are you a little confused about them? Or have you never heard of them and need to know what they are? If you need some help with piecewise functions, then you have come to the right place. This chapter is focused solely on these functions. You will get to study how they differ from other functions. You'll learn more about how these functions can be defined by different rules based upon the independent variable in the equation. Our lessons will provide you with numerous examples so that you can tackle this type of function easily. We will take the guesswork out of working with piecewise functions so that when you approach one in the future, you will know exactly how to handle it. Some of the things you can expect to learn in this chapter include:

  • The definition of piecewise functions
  • How piecewise functions compare with ordinary functions
  • The importance of the domain in a piecewise function
  • Graphing this type of function
  • Definitions for continuity and discontinuity
  • Applying translations to piecewise graphs

What Are Piecewise Functions? Discover what a piecewise function is and how it compares to an ordinary function.
How to Find the Domain of Piecewise Functions Study why the domain is the most important part of a piecewise function.
How to Graph Piecewise Functions Examine how to graph piecewise functions on one coordinate plane, and also learn about continuity and discontinuity.
Translating Piecewise Functions Explore how to apply translations to piecewise graphs and understand how they affect a functions domain.

6 Lessons in Chapter 8: Piecewise and Composite Functions
Test your knowledge with a 30-question chapter practice test
What are Piecewise Functions?

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.

How to Find the Domain of Piecewise Functions

2. How to Find the Domain of Piecewise Functions

The domain of any function is all the values that x can be for that function. Piecewise functions are special functions that have different parts with unique rules for each part. This lesson will show you how to find the domain for piecewise functions.

How to Graph Piecewise Functions

3. 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.

Translating Piecewise Functions

4. Translating Piecewise Functions

Piecewise functions are two or more functions that only use part of a domain. If these functions need to be changed, we can translate them without even having to know the equation.

How to Evaluate Composite Functions

5. How to Evaluate Composite Functions

Sometimes a math function depends on the outcome of another function. This lesson breaks down this chain reaction, called a composite function, and how to evaluate them.

Manipulating Functions and Solving Equations for Different Variables

6. 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.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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