Ch 21: AEPA Math: Functions

About This Chapter

Arizona uses the AEPA Math exam as a basis for the certification of mathematics teachers. This chapter's engaging lessons on functions will help you with solidifying your knowledge and correctly answering some questions on the exam.

AEPA Math: Functions - Chapter Summary

Strengthen your knowledge of functions before you take the AEPA Math exam. You'll see helpful examples and clear definitions for the domain and range of composite functions as you're studying the content in this chapter. Other information on functions brought to your attention via text and video lessons includes:

  • How to compose functions
  • Graphic, numeric and algebraic comparisons of function properties
  • Function addition, subtraction, multiplication and division
  • Even, odd and inverse functions
  • Different kinds of math transformations
  • Various ways to recognize symmetry about the x-axis and y-axis
  • Compounding functions and graphing functions of functions

Our professional instructors will make you more familiar with these topics through their effective teaching styles. The video lessons are short, and they express the text content to you in an easily understood way.

Objectives of the AEPA Math: Functions Chapter

Part of the AEPA Math exam's content is concerned with your knowledge of various functions topics. Questions that relate to functions can be found in the Patterns, Algebra and Functions content domain of the test, which is worth about 24% of the exam score. The test questions are all multiple-choice and there are 150 of them. The time limit set for getting through all the questions is 4 hours and 15 minutes. This computer-based exam has a scientific calculator that appears on the screen for your use and there is also a page with formulas to reference. Try this chapter's practice quizzes for a fast way to gauge your comprehension of functions before test day.

14 Lessons in Chapter 21: AEPA Math: Functions
Test your knowledge with a 30-question chapter practice test
Compare Properties of Functions Algebraically

1. 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

2. 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 Numerically

3. Compare Properties of Functions Numerically

Can you compare functions when they're written out numerically as tables of values? In this lesson, you'll learn to do just that and to compare one function as a table to another written in a different form.

Transformations: How to Shift Graphs on a Plane

4. 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?

5. 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 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.

Domain & Range of Composite Functions: Definition & Examples

8. 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.

Compounding Functions and Graphing Functions of Functions

9. 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!

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.

Recognizing Symmetry Graphically, Algebraically, and Numerically About the X-axis and Y-axis

12. Recognizing Symmetry Graphically, Algebraically, and Numerically About the X-axis and Y-axis

When you fold a piece of paper exactly in half, you are creating symmetry. Symmetry is found in many areas of mathematics. In this lesson, learn to recognize symmetry graphically, algebraically, and numerically about the x- and y- axes.

Recognizing Symmetry Graphically, Algebraically & Numerically About the Origin

13. Recognizing Symmetry Graphically, Algebraically & Numerically About the Origin

If you look at flowers and fruits, you'll see that many of these items in nature are symmetrical. In this lesson, learn about symmetry about the origin of a graph. When you are finished, test your knowledge with a short quiz!

Even & Odd Functions: Definition & Examples

14. Even & Odd Functions: Definition & Examples

Even and odd functions are an aspect of line symmetry. You can use knowledge of even and odd functions to quickly identify equation symmetry. After this lesson, test your knowledge with a short quiz!

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 AEPA Mathematics (NT304): Practice & Study Guide course

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