# Ch 19: NES Middle Grades Math: Properties of Functions

### About This Chapter

## NES Middle Grades Math: Properties of Functions - Chapter Summary

The animated video lessons in this chapter discuss functions topics such as inverse functions, domain and range, and function notation. As you get set to take the NES Middle Grades Math examination, explore the different kinds of transformations, study examples of function composition and learn more about the three forms of linear functions. Revisit the concepts in this chapter in order to:

- Explain the fundamentals and key terms of functions
- Shift graphs on a plane
- Perform addition, subtraction, multiplication and division operations with functions
- Learn more about domain and range
- Review the process of composing functions
- Find and write inverse functions
- Apply function operations
- Contrast linear and nonlinear functions

Knowledgeable teachers present these and other concepts throughout each of the short video lessons. Offered online, the videos can be studied at your convenience with the help of your desktop or laptop computer - or via a tablet. Build upon your comprehension of the properties of functions in advance of sitting for the NES Middle Grades Math examination. Utilize the navigational video tags, written transcripts and self-assessment quizzes that are included in the chapter.

### NES Middle Grades Math: Properties of Functions Chapter Objectives

The equivalent of 33% of the overall assessment score, the *Algebra and Functions* content domain of the NES Middle Grades Math examination evaluates your knowledge of the properties of functions. Your review of this chapter could prepare you to answer some of the examination's 150 multiple-choice questions. You'll have four hours and 15 minutes to finish the computerized assessment and to demonstrate your readiness to educate middle grade students in mathematics.

### 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.

### 2. 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!

### 3. 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!

### 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.

### 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.

### 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.

### 7. 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!

### 8. 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.

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### Other Chapters

Other chapters within the NES Middle Grades Mathematics (203): Practice & Study Guide course

- NES Middle Grades Math: Basic Arithmetic Operations
- NES Middle Grades Math: Solving Word Problems
- NES Middle Grades Math: Properties of Numbers
- NES Middle Grades Math: Estimating & Rounding
- NES Middle Grades Math: Number Theory
- NES Middle Grades Math: Roots & Radical Expressions
- NES Middle Grades Math: Exponents & Exponential Expressions
- NES Middle Grades Math: Scientific Notation
- NES Middle Grades Math: Simplifying Expressions
- NES Middle Grades Math: Integers
- NES Middle Grades Math: Rational Numbers
- NES Middle Grades Math: Introduction to Fractions
- NES Middle Grades Math: Operations with Fractions
- NES Middle Grades Math: Introduction to Decimals
- NES Middle Grades Math: Operations with Decimals
- NES Middle Grades Math: Percents
- NES Middle Grades Math: Money & Consumer Math
- NES Middle Grades Math: Number Patterns & Sequences
- NES Middle Grades Math: Graphing Functions
- NES Middle Grades Math: Negative Numbers
- NES Middle Grades Math: Absolute Value
- NES Middle Grades Math: Inequalities
- NES Middle Grades Math: Factoring
- NES Middle Grades Math: Monomials & Polynomials
- NES Middle Grades Math: Writing Algebraic Expressions
- NES Middle Grades Math: Basic Algebraic Expressions
- NES Middle Grades Math: Algebraic Distribution
- NES Middle Grades Math: One-Step Equations
- NES Middle Grades Math: Two-Step Equations
- NES Middle Grades Math: Rational Expressions
- NES Middle Grades Math: The Coordinate Graph
- NES Middle Grades Math: Linear Equations
- NES Middle Grades Math: Systems of Linear Equations
- NES Middle Grades Math: Rates, Ratios & Proportions
- NES Middle Grades Math: Measurement
- NES Middle Grades Math: Perimeter & Area
- NES Middle Grades Math: Polyhedrons & Geometric Solids
- NES Middle Grades Math: Symmetry, Similarity & Congruence
- NES Middle Grades Math: Properties of Lines
- NES Middle Grades Math: Angles
- NES Middle Grades Math: Triangles
- NES Middle Grades Math: Triangle Theorems & Proofs
- NES Middle Grades Math: Similar Polygons
- NES Middle Grades Math: The Pythagorean Theorem
- NES Middle Grades Math: Quadrilaterals
- NES Middle Grades Math: Circles
- NES Middle Grades Math: Circular Arcs & Measurement
- NES Middle Grades Math: Transformations
- NES Middle Grades Math: Data & Graphs
- NES Middle Grades Math: Statistics
- NES Middle Grades Math: Data Collection
- NES Middle Grades Math: Samples & Populations
- NES Middle Grades Math: Probability
- NES Middle Grades Math: Sets
- NES Middle Grades Mathematics Flashcards