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Ch 21: PLACE Mathematics: Functions

About This Chapter

As you prepare for the Colorado PLACE Mathematics certification exam, watch the lesson videos in this chapter on functions. Learn how to compose functions, graph functions and shifts graphs on a plane as part of your preparation.

PLACE Mathematics: Functions - Chapter Summary

As you prepare for the PLACE Mathematics exam, take time to learn how to work with functions through the engaging lesson videos in this chapter. Follow along with our instructors as they review the common properties of different mathematical functions, graphing techniques and how to complete mathematical operations with functions. If you become confused about a topic or have a question, make sure to ask our instructors so that you can effectively master the material on:

  • Algebraic, graphical and numeric properties of functions
  • Graphical transformations
  • The domain and range of functions and composite functions
  • Addition, subtraction, multiplication and division with functions
  • Composing and compounding functions
  • Inverse functions and graphing inverse functions
  • Recognizing symmetry graphically
  • Differences between even and odd functions

In additions to these lesson videos, this chapter includes quizzes you can use to fortify the material you reviewed. In addition, there are video tags that will take you directly to key topics in the lesson videos and transcripts that present the material of the videos in an easy to read format.

PLACE Mathematics: Functions Chapter Objectives

PLACE Mathematics is a four and a half hour, paper-based exam used in the state of Colorado. This test is composed of a series of multiple-choice questions, of which 24% make up the mathematical functions and relations section; this section is where you can find questions related to the topics in this chapter. Prepare for these questions by completing the lesson videos and quizzes in this chapter then fortify areas of weaknesses using easily to use video tags and lesson transcripts.

14 Lessons in Chapter 21: PLACE Mathematics: 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 PLACE Mathematics: Practice & Study Guide course

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