About This Chapter
Graphing Piecewise Functions - Chapter Summary and Learning Objectives
Video lessons and quizzes in this chapter build on your knowledge of regular functions to help you learn what it takes to write equations for piecewise functions and employ the special techniques used to graph them. Instructors take the time to walk you through the steps involved in each process and use plenty of illustrations to drive home important concepts. They can also help you examine the real-life applications of piecewise functions. By the end of this chapter, you should be able to do the following:
- Compare ordinary and piecewise functions
- Find a piecewise function's domain
- Graph and translate piecewise functions
|What Are Piecewise Functions?||Find out what a piecewise function is. Get tips for evaluating piecewise functions, and investigate their uses to calculate payments and solve other types of financial problems.|
|How to Find the Domain of Piecewise Functions||Learn how to find the domain of a piecewise function by examining its equations or its graph.|
|How to Graph Piecewise Functions||Explore methods for graphing a piecewise function on the coordinate plane.|
|Translating Piecewise Functions||Apply translations to shift a piecewise function's graph up, down, left and right. You can also learn how to stretch and reflect the graph of a piecewise function, and investigate how these transformations affect a function's domain.|
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 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.
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.
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.
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Other chapters within the Precalculus: High School course
- Working With Inequalities
- Absolute Value Equations
- Working with Complex Numbers
- Introduction to Quadratics
- Working with Quadratic Functions
- Basics of Polynomial Functions
- Working with Higher-Degree Polynomials
- Understanding Function Operations
- Graph Symmetry
- Graphing with Functions
- Rate of Change
- Rational Functions & Difference Quotients
- Rational Expressions and Function Graphs
- Exponential Functions & Logarithmic Functions
- Using Trigonometric Functions
- Trigonometric Graphs
- Trigonometric Applications
- Solving Trigonometric Identities
- Vectors, Matrices and Determinants
- Mathematical Sequences and Series
- Sets in Algebra
- Analytic Geometry and Conic Sections
- Polar Coordinates and Parameterizations