About This Chapter
Algebra Functions & Graphs - Chapter Summary
This chapter includes lessons on various aspects of functions and graphs encountered in algebra. You'll learn about what distinguishes numerous types of functions while looking at related components and their presence in algebraic graphs. Topics covered include arithmetic series, the domain and range of a function, and all of the following:
- Function notation
- Identifying functions
- Differentiating between linear and non-linear functions
- The functional relation between quantities
- Compounding and graphing functions of functions
- Graphing rational functions with polynomials of different degrees
- The components of a graph depicting a rational function
You'll find each of these lessons available in both video and text format, allowing you to learn the way that best fits your style. If you opt for the transcripts, you'll find bolded words throughout pointing out key terms and topics, while the timeline feature enables video-watchers to hop around main points of the content with ease.
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. How to Recognize Linear Functions vs Non-Linear Functions
In this lesson, you'll learn about two different groups of functions: linear and nonlinear. We'll cover how they look on a graph, and how you can tell them apart when they're written as equations.
4. Describe the Functional Relationship Between Quantities
In this lesson, you'll learn how to look at a graph, table, or function written mathematically and verbally describe the functional relationship shown. For example, you'll learn to describe whether the function is increasing or decreasing.
5. Understanding Arithmetic Series in Algebra
In this video lesson, we will learn about arithmetic series and how they work. Learn also how to find the pattern of an arithmetic sequence along with finding the sum.
6. Compounding Functions and Graphing Functions of Functions
We know that functions map numbers to other numbers, so what happens when you have a function of a function? Welcome to functions within functions, the realm of composite functions!
7. Graphing Rational Functions That Have Polynomials of Various Degrees: Steps & Examples
Graphing rational functions is not as hard or as scary as it sounds. Sure, the functions may be big, but watch this video lesson and you will see that graphing these functions can actually be easy.
8. Analyzing the Graph of a Rational Function: Asymptotes, Domain, and Range
A rational function arises from the ratio of two polynomial expressions. The graphs of rational functions often have distinct characteristics. In this lesson, we look at how to analyze some of those characteristics.
9. Composition of Functions: Definition & Examples
What is a composition of functions and exactly how do you solve them? Find out and practice solving them in this lesson, then test your skills and knowledge with a quiz.
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