About This Chapter
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.|
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.
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.
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.
Earning College Credit
Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.
To learn more, visit our Earning Credit Page
Transferring credit to the school of your choice
Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.
Other chapters within the Math 103: Precalculus course
- Evaluating Exponential and Logarithmic Functions
- Foundations of Linear Equations
- Graphing and Rational Equations
- Factoring and Graphing Quadratic Equations
- Exponents and Polynomials
- Geometry and Trigonometry
- How to Use a Scientific Calculator
- Studying for Math 103