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

### About This Chapter

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

This chapter focuses exclusively on the various properties of functions, including functions in graphs and standard equations. Some other relevant topics we'll cover include:

- A function's domain and range
- Composing functions
- Dealing with linear and nonlinear functions
- Adding and subtracting functions
- Inverse functions

With these video lessons, created by our subject-matter experts, it's never been easier to refresh your understanding of functions and their properties. Assess your skills at the end of each lesson, and reach out to our teachers any time you have a question.

### Objectives of the NMTA Middle Grades Math: Properties of Functions Overview Chapter

With the video lessons in this chapter, you'll be prepared for any function-related problem on the NMTA Middle Grades Math test. The test could include questions that ask you to analyze the effects of graph transformation on a function or work with functions in word problems, tables, equations and more.

You're given four hours and 15 minutes to answer all 150 multiple-choice questions in a computer-based format. The passing score is 220, and you'll know whether or not you passed upon completing the exam. Official score reports are typically released within two weeks.

### 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.

### Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

### Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

### Other Chapters

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

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