# Ch 21: Praxis Middle School Math: Functions

### About This Chapter

## Praxis Middle School Math: Functions - Chapter Summary

This series of short, engaging lesson videos will help you prepare for exam questions on the Praxis Middle School Mathematics exam involving functions. In these lesson videos, our professional instructors will explain the properties of functions and the procedures used to solve and graph them. Follow along to improve your understanding of:

- What a function is and the conditions that are required for a function to work
- Algebraic and numerical properties of functions
- Uses of tables and graphs to solve problems involving functions
- Calculations for the domain and range of a function
- How to compose functions
- Processes used to determine the relationship between two quantities and rate change
- Addition, subtraction, multiplication and division with functions
- How to solve problems with inverse functions

These lessons are mobile device-compatible, enabling you to watch them when you are away from your desk. Also, this chapter includes a series of lesson transcripts you may read to reinforce your retention of the material presented in them. To test your understanding of the material and discover topics you still may need to review, take the short lesson quizzes.

### 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. 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!

### 3. 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.

### 4. 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.

### 5. Using Tables and Graphs in the Real World

We use tables and graphs in algebra as ways to visually show an equation or function. But do we really use these in the real world? Is it that important to learn about tables and graphs? Find out in this video lesson.

### 6. T-Charts in Math: Examples & Problems

T-charts are great organizational tools to help solve equations with more than one variable. Whenever you have equations with unknowns, you can use a T-chart to organize and solve a problem.

### 7. 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.

### 8. Domain in Math: Definition & Overview

The domain is the group of numbers that can be entered into a function to create a valid output. This lesson will further describe the domain and methods for determining the domain. A quiz at the end of a lesson will test your knowledge.

### 9. Composing Functions: Definition and Examples

In this lesson, you'll learn the definition of a mathematical function and explore function notation and function tables. We will also review several examples of functions.

### 10. Model a Linear Relationship Between Two Quantities

In this lesson, we will learn about modeling linear relationships by converting domain and range values into ordered pairs and then constructing a graph.

### 11. Determine the Rate of Change of a Function

In this lesson, we will learn about the rate of change of a function with specific focus on linear and exponential functions while examining the graphs of both types of functions.

### 12. 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!

### 13. 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.

### 14. 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.

### 15. 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!

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### Other Chapters

Other chapters within the Praxis Middle School Mathematics (5169): Practice & Study Guide course

- Praxis Middle School Math: Number Basics
- Praxis Middle School Math: Rational Numbers
- Praxis Middle School Math: Properties of Numbers
- Praxis Middle School Math: Number Structure
- Praxis Middle School Math: Absolute Value
- Praxis Middle School Math: Equality
- Praxis Middle School Math: Arithmetic Operations
- Praxis Middle School Math: Introduction to Fractions
- Praxis Middle School Math: Operations with Fractions
- Praxis Middle School Math: Decimals
- Praxis Middle School Math: Percents
- Praxis Middle School Math: Ratios & Rate of Change
- Praxis Middle School Math: Proportional Relationships
- Praxis Middle School Math: Estimation
- Praxis Middle School Math: Scientific Notation & Exponents
- Praxis Middle School Math: Square Roots
- Praxis Middle School Math: Roots & Radicals
- Praxis Middle School Math: Algebra Basics
- Praxis Middle School Math: Principles of Algebra
- Praxis Middle School Math: Solving Word Problems
- Praxis Middle School Math: Linear Equations
- Praxis Middle School Math: Solving Linear Equations
- Praxis Middle School Math: Patterns in Math
- Praxis Middle School Math: Graphing Functions
- Praxis Middle School Math: Polynomials
- Praxis Middle School Math: Quadratic Equations
- Praxis Middle School Math: Systems of Equations
- Praxis Middle School Math: Area, Perimeter & Volume
- Praxis Middle School Math: Properties & Theorems
- Praxis Middle School Math: Parallel, Perpendicular & Intersecting Lines
- Praxis Middle School Math: Properties of Triangles
- Praxis Middle School Math: Similarity & Congruence
- Praxis Middle School Math: Quadrilaterals
- Praxis Middle School Math: Polygons
- Praxis Middle School Math: Circles
- Praxis Middle School Math: Coordinate Geometry
- Praxis Middle School Math: Measurement
- Praxis Middle School Math: Geometric Construction
- Praxis Middle School Math: Data
- Praxis Middle School Math: Line Graphs
- Praxis Middle School Math: Data Presentation
- Praxis Middle School Math: Probability
- Praxis Middle School Math: Logic
- Praxis Middle School Math: Modeling
- Praxis Middle School Mathematics Flashcards