About This Chapter
Types of Functions in Precalculus - Chapter Summary and Learning Objectives
In precalculus, there are a variety of function types to learn and understand. This chapter provides an in-depth look at these to help you prepare for quizzes and tests, or complete homework assignments. Each lesson explores a different type or aspect of a function to boost your knowledge at a pace that works for you. Review the lessons to better understand domain and range, power and radical functions and much more.
The video lessons in this chapter average 10 minutes each and feature full transcripts with easily identifiable vocabulary words. Review them in any sequence, and revisit as often as you'd like. If you need additional information about any lesson topic, feel free to submit your questions to our experts. Self-assessment quizzes and a chapter exam are available to gauge your understanding of this subject area. Once you've completed this chapter, you will comprehend the following:
- The basic and key terms of a function
- Identification and notation of functions
- The meaning of domain and range in a function
- Equations and graphs of a power and radical function
- The definition and graphs of reciprocal functions
|What is a Function: Basics and Key Terms||Describe how to use function notation and why it's useful.|
|Functions: Identification, Notation & Practice Problems||Explain the process of using function notation, and discuss why it's useful.|
|What Is Domain and Range in a Function?||Learn which values are not allowed in a function.|
|What is a Power Function? - Definition, Equations, Graphs & Examples||Discover how to write and graph power functions.|
|What is a Radical Function? - Definition, Equations & Graphs||Study the process of graphing square root and cube root functions.|
|Reciprocal Functions: Definition, Examples & Graphs||Define and explain how to graph reciprocal functions.|
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. Reciprocal Functions: Definition, Examples & Graphs
This lesson defines reciprocal functions and their general form. We'll look at examples of these types of functions and define their characteristics. We'll also examine how to use these characteristics to graph these types of functions.
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Other chapters within the Honors Precalculus Textbook course
- Working with Linear Equations
- Working With Inequalities
- Absolute Value Equations
- Working with Complex Numbers
- Systems of Linear Equations
- Mathematical Modeling for Precalculus
- Introduction to Quadratics
- Working with Quadratic Functions
- Geometry Basics for Precalculus
- Understanding Function Operations
- Graphing Functions in Precalculus
- Graph Symmetry
- Rate of Change
- Polynomial Function Basics in Precalculus
- Higher-Degree Polynomial Functions
- Rational Functions & Difference Quotients
- Rational Expressions & Function Graphs in Precalculus
- Exponential Functions & Logarithms in Precalculus
- Using Trigonometric Functions
- Trigonometric Graphs
- Solving Trigonometric Equations
- Trigonometric Identities
- Trigonometric Applications
- Graphing Piecewise Functions in Precalculus
- Vectors in Precalculus
- Matrices and Determinants in Algebra
- Understanding Arithmetic Sequences & Series
- Understanding Geometric Sequences & Series
- Analytic Geometry and Conic Sections
- Polar Coordinates and Parameterizations
- Working with Sequences & Series
- Sets & Probability
- Limits in Precalculus