Ch 13: CEOE Middle Level/Intermediate Math: Introduction to Functions

About This Chapter

The lessons in this chapter are for Oklahoma teachers and aspiring teachers as they prepare to take the Certification Examinations for Oklahoma Educators (CEOE) Middle Level/Intermediate Math test. This chapter is an introduction to functions.

CEOE Middle Level/Intermediate Math: Introduction to Functions - Chapter Summary

Our subject matter experts put together these video and text lessons as refreshers before taking the CEOE Middle Level/Intermediate Math test. They will prep the student for questions that could be on the test about functions from material discussed in the lessons, including:

  • Identification and notation of functions
  • How to graph basic functions
  • Understanding the function domain and range
  • Use of graph transformations
  • The functions of addition, subtraction, multiplication and division
  • Composing functions
  • Understanding compounding functions and graphing functions of functions
  • The domain and range of composite functions
  • An explanation of inverse functions
  • How to use and graph inverse functions
  • What one-to-one functions are, including examples
  • How to find minima and maxima
  • Comparing properties of functions both algebraically and graphically

The videos average 5-10 minutes and come with a transcript There is a keyword-base timeline tool for simplicity of returning to any specific spot on the video you want to review. Both text and video lessons provide quizzes at the end to test your comprehension of the material. We have a feature that allows you to ask questions of an expert.

15 Lessons in Chapter 13: CEOE Middle Level/Intermediate Math: Introduction to Functions
Test your knowledge with a 30-question chapter practice test
Functions: Identification, Notation & Practice Problems

1. 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!

Function Table in Math: Definition, Rules & Examples

2. Function Table in Math: Definition, Rules & Examples

Functions can be represented in four different ways. In this lesson, we will learn what a function table is, and how and when to use a function table to represent a function. We will also explore the rules that define a given function table.

Graphing Basic Functions

3. Graphing Basic Functions

Graphs are just like maps - when you know the language! Review how locations have x and y coordinates similar to latitude and longitude, and how to plot points in the Cartesian plane.

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.

Transformations: How to Shift Graphs on a Plane

5. 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

6. 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!

How to Compose Functions

7. 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.

Compounding Functions and Graphing Functions of Functions

8. Compounding Functions and Graphing Functions of Functions

We know that functions map numbers to other numbers, so what happens when you have a function of a function? Welcome to functions within functions, the realm of composite functions!

Domain & Range of Composite Functions: Definition & Examples

9. Domain & Range of Composite Functions: Definition & Examples

Learn what makes a function a composite function and also learn how the parts of a composite function determine its domain. Also in this video lesson, learn about the range of composite functions.

Inverse Functions

10. 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.

Understanding and Graphing the Inverse Function

11. Understanding and Graphing the Inverse Function

If you use a function to map a to b, is there a way to go back from b to a again? Learn how to find and graph inverse functions so that you can turn a into b and back into a.

One-to-One Functions: Definitions and Examples

12. 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.

Finding Minima & Maxima: Problems & Explanation

13. Finding Minima & Maxima: Problems & Explanation

One of the most important practical uses of higher mathematics is finding minima and maxima. This lesson will describe different ways to determine the maxima and minima of a function and give some real world examples.

Compare Properties of Functions Graphically

14. 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.

Compare Properties of Functions Algebraically

15. 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.

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 OSAT Middle Level/Intermediate Mathematics (CEOE) (125): Practice & Study Guide course

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