About This Chapter
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.
1. Domain in Math: Definition & Overview
The domain is the group of numbers that can be entered into a function to create a valid output. This lesson will further describe the domain and methods for determining the domain. A quiz at the end of the lesson will test your knowledge.
2. What is Range in Math? - Definition & Meaning
The range of a function is the set of values that are produced by that function. This lesson will define and describe how to determine the range and will also give some examples.
3. Range of Values: Definition & Overview
Discover how easy it is to find the range of values in a given set. Learn how you can explain range to yourself and others and how you can use it to gain useful information.
4. Using Recursive Rules for Arithmetic, Algebraic & Geometric Sequences
When dealing with sequences in math, both algebraic and geometric, we come across recursive rules. Watch this video lesson to learn how recursion works and how you can use a recursive rule to get to your next number using a previous number.
5. 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.
6. 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.
7. 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.
8. Translating Piecewise Functions
Piecewise functions are two or more functions that only use part of a domain. If these functions need to be changed, we can translate them without even having to know the equation.
9. How to Evaluate Composite Functions
Sometimes a math function depends on the outcome of another function. This lesson breaks down this chain reaction, called a composite function, and how to evaluate them.
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Other chapters within the MTTC Professional Readiness Examination (096): Practice & Study Guide course
- Basic Number Sense
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- Mathematical Reasoning & Problem-Solving
- Logic in Mathematics
- Expressions, Functions & Operations
- Expressions & Equations in Algebra
- Using Algebraic Functions
- Polynomials, Rational Equations & Trigonometric Equations
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- Measuring Geometric Figures
- Relationships Between Figures in Geometry
- Basics of Trigonometry
- Fundamentals of Statistics
- Bivariate Relationships in Statistics
- Using Tables & Graphs
- Interpreting Statistical Data
- Probability Overview
- Introduction to Conditional Probability & Diagrams
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- Strategies for Effective Writing
- Reading Strategies & Literary Analysis
- Critical Reasoning for Test-Taking
- Conventions in Writing: Effective Usage
- Constructing Sentences & Paragraphs
- Argumentative Writing Overview
- Structuring Informational & Explanatory Texts
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