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Ch 8: Understanding Algebraic Functions

About This Chapter

In this chapter, you will get reacquainted with algebraic functions and their uses. As you follow along with the instructors in the lessons, you will see how the different functions are used in the related formulas.

Understanding Algebraic Functions - Chapter Summary

To prove your mastery of mathematics, you will have to show how well you remember and understand some of the more fundamental lessons, such as algebraic functions. The information from this chapter has been designed to help you recall basic terminology and equations associated with algebraic functions. At the end of the chapter, you should have no issues answering questions about the following:

  • Definitions for domain and range
  • The definition of the range of values
  • How to implement the recursive rules for sequences
  • The purpose of piecewise functions and the process of identifying their domain
  • Translating and graphing piecewise functions
  • Composite functions analysis

We've created these materials with certain goals in mind, and one of those goals includes giving you practical and effective tools. After all, no matter how elaborate a study guide may be, if it's not practical for the user, it's virtually useless. That's why we keep our learners in mind, and we give you what you need. This includes video lessons and transcripts that are available 24/7 on an online platform that you can access any time from practically any location.

The tools we provide to you are effective because they address your needs. For instance, you are most likely preparing for some sort of test or assessment, so these chapters are basically a recap of information you should already know. We understand that you don't have to relearn everything and that you just need to touch on a few topics that are less familiar. That's why we break all of our chapters into smaller lessons. You can look through the lesson titles to find the exact areas you need to review. This keeps you from wasting time reading through information you already know.

9 Lessons in Chapter 8: Understanding Algebraic Functions
Test your knowledge with a 30-question chapter practice test
How to Find the Domain of a Function

1. How to Find the Domain of a Function

A function is the relationship between an input and output. The domain of a function is the function's input, and the output of a function is the function's range. Learn how to find the domain of the function with either algebra or graphing, and how to write domain notation.

What is Range in Math? - Definition & Meaning

2. What is Range in Math? - Definition & Meaning

In math, the range refers to the outputs of a function, while the inputs are called the domain of the function. Learn about the definition and meaning of a range and the domain and range of a function, the three ways to determine a range, and its notation.

Range of Values: Definition & Overview

3. Range of Values: Definition & Overview

A range of values involves the scope of values in a given set, regardless of how many or few values populate the set. Explore the defining characteristics of a range of values, how to find the range, and a few examples to learn the process.

Using Recursive Rules for Arithmetic, Algebraic & Geometric Sequences

4. Using Recursive Rules for Arithmetic, Algebraic & Geometric Sequences

Recursive rules are found in arithmetic, algebraic and geometric sequences. A recursive rule takes a previous number and changes it to get a next number. Discover how the recursive rule works and learn how to use it in calculations through examples.

What are Piecewise Functions?

5. What are Piecewise Functions?

Piecewise functions have several parts, or pieces and are defined by a domain. Discover more about piecewise functions, some examples, how to evaluate them, and their application in the real world.

How to Find the Domain of Piecewise Functions

6. How to Find the Domain of Piecewise Functions

There are two ways to find the domain of a piecewise function: through its equation and its graph. Learn about the domain, piecewise functions, and more about the two ways to find the domain of piecewise functions.

How to Graph Piecewise Functions

7. How to Graph Piecewise Functions

Piecewise functions are mathematical operations that require multiple formulas, calculated in steps, to compute the final output. Learn about piecewise functions and work through examples to learn how to graph piecewise functions. Also recognize that piecewise functions may occur in pairs of equations or include three or more equations.

Translating Piecewise Functions

8. Translating Piecewise Functions

Combining bits and pieces of functions or graphs together is known as piecewise functions. Explore this concept through unknown piecewise functions, see formulas used in stretching reflecting and shifting, and how to translate them in visual transformations on the graph.

How to Evaluate Composite Functions

9. How to Evaluate Composite Functions

Multiple mathematic functions can be combined into a composite function where the value of one function depends on the other. Learn how to write, define, and evaluate composite functions with a series of examples.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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More Exams
There are even more practice exams available in Understanding Algebraic Functions.

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