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Ch 24: MTEL Mathematics (Elementary): Properties of Functions

About This Chapter

Use the materials available in these lessons to review the related information needed to be successful on the Massachusetts Test for Educator Licensure for Mathematics (Elementary). This chapter focuses on concepts that will help you prepare for Subarea II of the test.

MTEL Mathematics(Elementary): Properties of Functions - Chapter Summary

Sub-area II on the MTEL Mathematics (Elementary) focuses on patterns, relations, and algebra. Properties of functions is the topic under this sub-area that these lessons will help you to better understand. The lessons in this chapter will provide information on functions, allowing you to practice related skills. Topics covered include:

  • Background information on functions
  • The rate of change of a function
  • Comparison of functions graphically and algebraically
  • Shifting graphs on a plane
  • Domain and range in a function
  • Graphing functions
  • Subtraction, multiplication and division of functions
  • Identification, notation and practice problems

As you complete the lesson, use features such as ask an expert to aid in your progress; the personal dashboard will help you track your progress. The addition of this study guide to any other resources you are using will help you gain certification.

9 Lessons in Chapter 24: MTEL Mathematics (Elementary): 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.

Determine the Rate of Change of a Function

2. Determine the Rate of Change of a Function

In this lesson, we will learn about the rate of change of a function with specific focus on linear and exponential functions while examining the graphs of both types of functions.

Compare Properties of Functions Algebraically

3. Compare Properties of Functions Algebraically

In this lesson, we will explore algebraic and numeric properties and the evaluation of functions. We'll demonstrate function evaluations and the idea that every element of the domain has a unique element in the range.

Compare Properties of Functions Graphically

4. Compare Properties of Functions Graphically

In this lesson, we will cover the characteristics of graphs of functions. We will employ the vertical line test and understand why some graphs do not qualify as functions.

Graph Functions by Plotting Points

5. Graph Functions by Plotting Points

Let's say you have a function. What does it look like? How do you graph it? In this lesson, we'll learn how to graph functions by determining and plotting points.

Transformations: How to Shift Graphs on a Plane

6. 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!

How to Add, Subtract, Multiply and Divide Functions

7. 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!

What Is Domain and Range in a Function?

8. 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.

Functions: Identification, Notation & Practice Problems

9. 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!

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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Other Chapters

Other chapters within the MTEL Mathematics (Elementary) (53): Practice & Study Guide course

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