About This Chapter
Functions for Trigonometry- Chapter Summary and Learning Objectives
In these lessons, we'll learn what functions are in trigonometry and how to use them. Several lessons cover piecewise functions as well as transformations. This chapter also includes some practice problems in function identification and notation, giving you a change to check what you've studied. By the conclusion of this chapter, you should have a solid understanding of:
- Function notation and when it can be used
- Definition of power function and radical function
- Finding the domain of piecewise functions
- Working with transformations
|What is a Function? Basics and Key Terms||In this lesson, you'll learn the vocabulary needed to work with functions as well as get some information on function notation.|
|Functions: Identification, Notation and Practice Problems||Here, we'll look at how to identify a function as well as use function notation. Practice problems are included, too.|
|What is Domain and Range in a Function?||We'll discuss the meaning of the terms 'domain' and 'range' and examine what values can't be used in a function.|
|What is a Power Function? - Definition, Equations, Graphs and Examples||You can find out what a power function is as well as discover how to write and graph their equations.|
|What is a Radical Function? - Definition, Equations and Graphs||In this lesson, we'll look at how to graph square root and cube root functions.|
|Discontinuities in Functions and Graphs||We'll look at discontinuities seen in graphs, especially point, jump and asymptotic discontinuities.|
|How to Graph Piecewise Functions||Here, we'll examine the process of graphing a piecewise function, which is different from a regular function.|
|How to Find the Domain of Piecewise Functions||Continuing with our work in piecewise functions, we'll see the process for determining their domain.|
|Transformations: How to Shift Graphs on a Plane||This lesson covers the definition of transformations and how they can be moved on a graph.|
1. What is a Function: Basics and Key Terms
Mapping numbers sounds complex, but we do it when we buy gasoline. We pump gasoline, and the gas station charges us based on the amount of gas that we pump. Learn how this relates to functions while reviewing the basics and notations in this lesson.
2. Functions: Identification, Notation & Practice Problems
A function is simply a rule that takes one number and turns it into another. But some special conditions must apply for it to be a true mathematical function. Learn about those conditions and how we write functions here!
3. What Is Domain and Range in a Function?
The domain and range are the possible outputs and inputs of a function. In this lesson, learn about what might restrict the domain and how to figure out the domain and range from a graph.
4. What is a Power Function? - Definition, Equations, Graphs & Examples
Power functions have many different varieties of graphs. Use this lesson to distinguish the difference between different types of power functions. Test your knowledge with a short quiz after the lesson!
5. What is a Radical Function? - Definition, Equations & Graphs
Radical functions operate very differently than regular functions. This lesson covers the definitions, equations, and graphs that you will need to know to be successful with radical functions.
6. Discontinuities in Functions and Graphs
In this lesson, we talk about the types of discontinuities that you commonly see in functions. In particular, learn how to identify point, jump and asymptotic discontinuities.
7. 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.
8. 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.
9. Transformations: How to Shift Graphs on a Plane
What is a transformation? Well, it's something that transforms one function into another! To see what I mean and how that looks, check out this lesson!
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Other chapters within the Trigonometry: High School course
- Real Numbers: Types and Properties
- Absolute Value Equations
- Working with Complex Numbers
- Coordinate Geometry Review
- Systems of Linear Equations
- Mathematical Modeling
- Introduction to Quadratics
- Understanding Function Operations
- Graph Symmetry
- Graphing with Functions
- Polynomial Functions Basics
- Exponential Functions & Logarithmic Functions
- Using Trigonometric Functions
- Triangle Trigonometry
- Trigonometric Graphs
- Solving Trigonometric Equations
- Trigonometric Identities
- Trigonometric Applications
- Analytic Geometry and Conic Sections
- Polar Coordinates and Parameterizations
- Circular Arcs, Circles & Angles
- Teaching Resources for High School Trigonometry