About This Chapter
Basics of Functions - Chapter Summary
This chapter serves as a fantastic resource for all things functions! Review engaging lessons that cover types of functions like linear, radical, quadratic, exponential and polynomial. Explore definitions and examine clear examples of these functions along with other related concepts. In no time, you will be prepared to do the following:
- Identify and notate functions
- Define domain and range in a function
- Pinpoint where a function is linear, increasing or decreasing, positive or negative
- Find and apply the intercepts of a line
- Use differentiation to find minimum and maximum values
- Understand what makes vertical and horizontal asymptotes unique
- Describe the behavior of exponential and logarithmic functions
- Share the meaning of linear, rational, radical, exponential, logarithmic and piecewise functions
- Write quadratic functions, and factor polynomial functions
Enjoy the ability to learn the basics of functions from home or on-the-go. The lessons are accessible from any computer or mobile device wherever you can access the Internet. Take advantage of other resources in this chapter, including short quizzes you can take to assess your knowledge lesson concepts. A comprehensive chapter exam is also available to gauge your understanding of functions.
1. 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!
2. 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.
3. Identify Where a Function is Linear, Increasing or Decreasing, Positive or Negative
Functions do all kinds of fun things. In this lesson, learn how to identify traits of functions such as linear or nonlinear, increasing or decreasing and positive or negative.
4. How to Find and Apply the Intercepts of a Line
How can you take an equation of a line and find out where it will cross the x- or y-axis? In this lesson, we'll define x-intercepts and y-intercepts and learn how to find them.
5. Using Differentiation to Find Maximum and Minimum Values
If you are shot out of a cannon, how do you know when you've reached your maximum height? When walking through a valley, how do you know when you are at the bottom? In this lesson, use the properties of the derivative to find the maxima and minima of a function.
6. Horizontal and Vertical Asymptotes
No matter how hard you try to get to them, asymptotes remain out of reach. Learn about these invisible lines on graphs that show you places your equations just can't go.
7. Behavior of Exponential and Logarithmic Functions
After watching this video lesson, you will be able to recognize exponential and logarithmic functions by looking at the end behavior of the graphs. You will also learn how the graphs change.
8. What is a Linear Function? - Definition & Examples
In this lesson, you will learn the key identifying mark of linear functions. You'll also learn how to graph them with just two points and how you can use the graph to easily find your answers.
9. Rational Function: Definition, Equation & Examples
Rational functions are an extremely useful type of function found in mathematics. They are functions that are fractions whose numerator and denominator are both polynomials. Learn all about them in this lesson!
10. 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.
11. How to Write Quadratic Functions
In the real world, you won't always be given equations as you are in textbooks. Often, you'll need to find equations using a few points or other pieces of data. Learn how to find and write quadratic equations.
12. Polynomial Functions: Properties and Factoring
Everything from projectile motion to trigonometric functions can be described by polynomials. Review factoring, polynomials and quadratic functions in this lesson.
13. What Is an Exponential Function?
Brand new technologies don't always catch on right away because they can be expensive and don't always work as well as they should. But once the price comes down, and they start to work better, it doesn't take very long before it seems like everyone has one. Learn about the numbers behind this, exponential functions!
14. Logarithmic Function: Definition & Examples
Exponential functions and logarithmic functions are closely tied. In fact, they are so closely tied we could say a logarithm is actually an exponent in disguise. A logarithm, or log, is just another way to write an exponential function in reverse.
15. 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.
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