Ch 19: MTEL Math: Properties of Functions

About This Chapter

The Properties of Functions is part of our MTEL Mathematics exam preparation course. Whether you're completely lost with properties of functions or you just need a review, our study guide offers several ways to help you get on track before exam day.

MTEL Mathematics: Properties of Functions- Chapter Summary

In this chapter, our expert instructors will show you the properties of mathematical functions, and go in-depth on the concepts behind functions. The Properties of Functions chapter has lessons on:

  • Defining functions
  • Identification, notation and practice problems for functions
  • Transformations
  • Domain and range in a function
  • Composing functions
  • Inverse functions
  • Linear and nonlinear functions
  • Power functions
  • Radical functions
  • One-to-one functions
  • Adding, subtracting, dividing, and multiplying functions
  • Applying function operations
  • Manipulating functions and solving equations for variables

Our expert-led video lessons will help you solidify your understanding of functions. You can watch them anytime, on a computer or mobile device. Multiple-choice lesson quizzes let you check your knowledge, and our instructors are available to answer questions.

13 Lessons in Chapter 19: MTEL Math: Properties of Functions
Test your knowledge with a 30-question chapter practice test
What is a Function: Basics and Key Terms

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.

Functions: Identification, Notation & Practice Problems

2. 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!

Transformations: How to Shift Graphs on a Plane

3. Transformations: How to Shift Graphs on a Plane

What is a transformation? Well, it's something that transforms one function into another! To see what I mean and how that looks, check out this lesson!

What Is Domain and Range in a Function?

4. 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.

How to Compose Functions

5. 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.

Inverse Functions

6. 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.

Linear and Nonlinear Functions

7. Linear and Nonlinear Functions

After watching this video lesson, you'll be able to tell the differences between linear and nonlinear functions. You'll also be able to identify both types just by looking at graphs.

What is a Power Function? - Definition, Equations, Graphs & Examples

8. What is a Power Function? - Definition, Equations, Graphs & Examples

Power functions have many different varieties of graphs. Use this lesson to distinguish the difference between different types of power functions. Test your knowledge with a short quiz after the lesson!

What is a Radical Function? - Definition, Equations & Graphs

9. 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.

One-to-One Functions: Definitions and Examples

10. One-to-One Functions: Definitions and Examples

Watch this video lesson to learn what makes a one-to-one function different from a regular function. Learn a simple test you can use to check whether a function is one-to-one or not.

How to Add, Subtract, Multiply and Divide Functions

11. How to Add, Subtract, Multiply and Divide Functions

Adding, subtracting, multiplying and dividing functions is about as simple as substituting in expressions and then just doing whichever operation it asks you to do. Check out this video lesson to see some examples of this and learn just how easy it is!

Applying Function Operations Practice Problems

12. Applying Function Operations Practice Problems

In this lesson, learn how to apply all the different properties of functions to solve complex problems. From function operations and composition to domain and range, get your practice here!

Manipulating Functions and Solving Equations for Different Variables

13. Manipulating Functions and Solving Equations for Different Variables

Functions can be manipulated to solve for many different variables. There are certain rules to follow, but if the rules are adhered to, solving equations can be quite simple. This lesson will show you how.

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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