About This Chapter
Functions Overview - Chapter Summary and Learning Objectives
In the lessons in this chapter, you'll get a basic understanding of what a function is. You'll learn about domain and range, graphing basic functions and transformations. Other lessons cover piecewise functions and discontinuities in functions and graphs. Practice problems will allow you to assess your knowledge. At the end of this chapter you should be able to:
- Understand the basic principles of functions and define important terms
- Graph basic, power, piecewise and radical functions
- Define domain and range in functions
- Shift graphs on a plane
- Find the domain of a piecewise function
|What is a Function: Basics and Key Terms||Learn facts and important terms in relation to functions|
|Functions: Identification, Notation and Practice Problems||Learn to identify and write equations for functions and practice these skills|
|Graphing Basic Functions||Learn to graph basic functions|
|What is Domain and Range in a Function||Identify and understand domain and range.|
|What is a Power Function: Equations and Graphs||Write and graph power functions.|
|What is a Radical Function: Equations and Graphs||Graph square root and cube root functions.|
|Discontinuities in Functions and Graphs||Learn to identify graph discontinuities.|
|How to Graph Piecewise Functions||Learn to graph piecewise functions.|
|How to Find the Domain of Piecewise Functions||Learn to determine the domain of a piecewise function.|
|Transformations: How to Shift Graphs on a Plane||Learn the methods to change 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. Graphing Basic Functions
Graphs are just like maps - when you know the language! Review how locations have x and y coordinates similar to latitude and longitude, and how to plot points in the Cartesian plane.
4. 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.
5. 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!
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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!
12. Greatest Integer Function: Definition & Examples
In this lesson, we'll examine the greatest integer function. We'll define this function through words and examples, and lastly, we'll take a look at different real world scenarios when this type of function can be used.
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Other chapters within the Math 105: Precalculus Algebra course
- Mathematical Modeling
- Linear Equations & Inequalities
- Quadratic Functions
- Rational Expressions and Functions
- Polynomial Functions of a Higher Degree
- Absolute Value Equations & Inequalities
- Complex Numbers
- Geometry Basics
- Function Operations
- Graph Symmetry
- Exponential and Logarithmic Functions
- Introduction to the Derivative
- Studying for Math 105