# Ch 24: MTEL Mathematics (Elementary): Properties of Functions

### About This Chapter

## MTEL Mathematics(Elementary): Properties of Functions - Chapter Summary

Sub-area II on the MTEL Mathematics (Elementary) focuses on patterns, relations, and algebra. Properties of functions is the topic under this sub-area that these lessons will help you to better understand. The lessons in this chapter will provide information on functions, allowing you to practice related skills. Topics covered include:

- Background information on functions
- The rate of change of a function
- Comparison of functions graphically and algebraically
- Shifting graphs on a plane
- Domain and range in a function
- Graphing functions
- Subtraction, multiplication and division of functions
- Identification, notation and practice problems

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### 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. 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.

### 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. Graph Functions by Plotting Points

Let's say you have a function. What does it look like? How do you graph it? In this lesson, we'll learn how to graph functions by determining and plotting points.

### 6. 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!

### 7. 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!

### 8. 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.

### 9. 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!

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### Other Chapters

Other chapters within the MTEL Mathematics (Elementary) (53): Practice & Study Guide course

- MTEL Mathematics (Elementary): Number Sense
- MTEL Mathematics (Elementary): Mathematical Operations
- MTEL Mathematics (Elementary): Factoring & Divisibility
- MTEL Mathematics (Elementary): Real Numbers
- MTEL Mathematics (Elementary): Prime Factorization
- MTEL Mathematics (Elementary): Rational Numbers
- MTEL Mathematics (Elementary): Properties of Numbers
- MTEL Mathematics (Elementary): Roots
- MTEL Mathematics (Elementary): Exponents
- MTEL Mathematics (Elementary): Exponential Expressions & Scientific Notation
- MTEL Mathematics (Elementary): Absolute Value
- MTEL Mathematics (Elementary): Integers
- MTEL Mathematics (Elementary): Estimating & Rounding
- MTEL Mathematics (Elementary): Principles of Fractions
- MTEL Mathematics (Elementary): Operations with Fractions
- MTEL Mathematics (Elementary): Introduction to Decimals
- MTEL Mathematics (Elementary): Operations with Decimals
- MTEL Mathematics (Elementary): Percents
- MTEL Mathematics (Elementary): Descriptive Statistics
- MTEL Mathematics (Elementary): Summarizing Data
- MTEL Mathematics (Elementary): Principles of Sampling
- MTEL Mathematics (Elementary): Regression & Correlation
- MTEL Mathematics (Elementary): Principles of Probability
- MTEL Mathematics (Elementary): Understanding Algebraic Expressions
- MTEL Mathematics (Elementary): Solving Algebraic Equations
- MTEL Mathematics (Elementary): Properties of Linear Relations
- MTEL Mathematics (Elementary): Graphing Linear Equations
- MTEL Mathematics (Elementary): Properties of Ratios & Proportions
- MTEL Mathematics (Elementary): Properties of Polynomial Functions
- MTEL Mathematics (Elementary): Properties of Quadratic Functions
- MTEL Mathematics (Elementary): Properties of Rational Functions
- MTEL Mathematics (Elementary): Properties of Exponential Functions
- MTEL Mathematics (Elementary): Principles of Measurement
- MTEL Mathematics (Elementary): Principles of Geometry
- MTEL Mathematics (Elementary): Understanding Lines in Geometry
- MTEL Mathematics (Elementary): Principles of Geometric Figures
- MTEL Mathematics (Elementary): Properties of Triangles
- MTEL Mathematics (Elementary): Proof of Theorems
- MTEL Mathematics (Elementary): Quadrilaterals
- MTEL Mathematics (Elementary): Polygons
- MTEL Mathematics (Elementary): Circles & Circular Arcs
- MTEL Mathematics (Elementary): Principles of Geometric Solids
- MTEL Mathematics (Elementary): Parallel Lines & Symmetry
- MTEL Mathematics (Elementary): Transformations in Geometry
- MTEL Mathematics (Elementary): Understanding Coordinate Geometry
- MTEL Mathematics (Elementary School) Flashcards