About This Chapter
Properties & Operations of Functions - Chapter Summary
The videos included in this helpful chapter outline the operations and properties of functions. Take your time as you review subjects such as polynomials functions, rational functions, inequalities and equations with rational functions, and more. This chapter is designed to assist you as you work to achieve the following:
- Describe the basics and key terms associated with a function
- Provide an overview of function operations
- Understand how to compose functions
- Describe inverse functions and their use
- Explain the properties as well as the factoring and simplification processes associated with polynomials functions
- Detail the equations used with rational functions
- Solve inequalities and equations involving rational functions
- Discuss how to solve logarithmic and exponential equations
Our study resources take the stress out of learning even the most challenging topics by breaking these concepts down into concise, bite-sized video lessons you can work on at your own pace. Each one is accompanied by a multiple-choice quiz to help you assess your understanding and determine where more study is needed. Feel free to access these materials 24/7 on your mobile device or computer.
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. Function Operation: Definition & Overview
In this lesson, we will define functions and determine how to use specific rules for the addition, subtraction, multiplication, and division of functions.
3. How to Compose Functions
Function composition is the process of putting two or more functions together. This video lesson will explain how this process works and also show you how to evaluate functions that have been composed.
4. Inverse Functions
Inverse functions are two functions that do exactly opposite things. Check out this lesson to learn about how to write inverse functions, find inverse functions, and predict whether or not they exist.
5. 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.
6. Polynomial Functions: Exponentials and Simplifying
How do we keep track of a rapidly multiplying population of bunnies? Well, those are simply powers of 2. Review powers and simplify problems with exponents in this lesson.
7. 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!
8. Solving Equations & Inequalities Involving Rational Functions
After watching this video lesson, you will be able to solve both equations and inequalities that involve rational functions. Learn the steps involved in solving them as well as what to watch out for.
9. How to Solve Exponential Equations
Read this lesson to learn the steps you need to take to solve exponential equations. You'll see that it's not too difficult; you just need to make use of one other mathematical operation in order to solve your problems.
10. How to Solve Logarithmic Equations
If you're ever picking out a telescope to see your favorite planet, make sure you do the math first! Learn how to solve the logarithmic equation that will get you the size telescope you want.
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Other chapters within the ILTS Elementary Education (Grades 1-6) (197-200, 305): Practice & Study Guide course
- Foundations of Literacy
- Language Features & Acquisition
- Selecting Materials for Literacy Instruction
- Developing Emergent Literacy Skills
- Literacy Assessment & Differentiation
- Phonological & Phonemic Awareness
- Decoding & Fluency Teaching Strategies
- Language & Reading Comprehension
- Vocabulary Acquisition & Use
- Reading Comprehension Instructional Strategies
- Analyzing Literary & Informational Texts
- Instructional Strategies for Literary & Text Analysis
- English Grammar Writing Conventions
- Writing Instruction & Feedback
- Instructional Strategies for Different Types of Writing
- Strategies for Teaching Speaking & Listening Skills
- Teaching Counting, Cardinality, Numbers & Operations
- Fraction Operations
- Teaching Operations & Algebraic Thinking
- Overview of Concepts in Algebra
- Principles of Operations & Algebraic Thinking
- Geometry Concepts
- Data Distribution & Graphs
- Permutation & Combination
- Interpreting Statistical & Probability Data
- Mathematical Development & Curriculum
- Measurement & Data
- Scientific Models & Relationships
- Scientific Inquiry & Lab Safety
- Evaluating Scientific Information
- Fundamental Concepts of Physical Science
- Fundamentals of Life Science
- Fundamentals of Earth & Space Science
- Overview of Government & Citizenship
- Overview of Economics & Political Principles for Illinois Educators
- Overview of History & Cultural Development for Illinois Educators
- Fundamentals of Human Geography for Illinois Educators
- Overview of the Arts for Educators
- Overview of Physical Education
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- Personal, Family & Community Health Overview for Educators
- Illinois Learning Standards
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