# Ch 6: Explorations in Core Math Algebra 2 Chapter 6: Properties and Attributes of Functions

### About This Chapter

## Explorations in Core Math Algebra 2 Chapter 6: Properties and Attributes of Functions - Chapter Summary and Learning Objectives

Compare and contrast different properties of functions with this chapter. You can also assess the attributes of functions. Studying these lessons will enable you to learn more about:

- Rate and exponential growth
- Numeric, algebraic and graphic properties of functions
- Piecewise functions and how they're graphed
- Function transformations
- How to perform algebraic operations on functions
- Quadratic models, cube root functions and quadratic and inverse relationships

Lesson | Objective |
---|---|

Calculating Rate and Exponential Growth: The Population Dynamics Problem | Learn how to calculate rate and exponential growth with real world examples. |

Compare Properties of Functions Numerically | Find out how to numerically compare properties of functions. |

Compare Properties of Functions Algebraically | Assess the properties of functions algebraically. |

Compare Properties of Functions Graphically | Evaluate the properties of functions graphically. |

What are Piecewise Functions? | Consider the definition and description of a piecewise function. |

How to Graph Piecewise Functions | Break down the special procedure for graphing piecewise functions. |

Comparing Function Transformations | Distinguish between function transformations. |

How to Add, Subtract, Multiply and Divide Functions | Focus on mastering the ability to perform algebraic operations on functions. |

Applying Function Operations Practice Problems | Test your ability to apply the properties of functions. |

Quadratic & Inverse Relationships | Develop the ability to tell when variables are in a quadratic or inverse relationship. |

Inverses of Cube Root Functions | Determine how to find the inverse of a cube root function. |

Quadratic Models: Inverse & Vertex Form | Evaluate different uses of the inverse and vertex forms of quadratic models. |

### 1. Calculating Rate and Exponential Growth: The Population Dynamics Problem

You know how the world population keeps increasing? It's increasing faster now than it was 100 or 1,000 years ago. In this lesson, learn how differential equations predict this type of exponential growth.

### 2. 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.

### 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. What are Piecewise Functions?

A piecewise function is a certain type of function that is made up of different parts. This lesson will define and describe piecewise functions and teach you how to identify them and how to write them.

### 6. How to Graph Piecewise Functions

Piecewise functions are specific functions that have more than one piece. There is a special trick to graphing these type of functions, which you will learn in this lesson.

### 7. Comparing Function Transformations

Transformations of functions are useful in the analysis of functions. This lesson explains how transformations compare for different types of functions. Then, we will look at transformations of exponential functions, specifically.

### 8. 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!

### 9. 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!

### 10. Quadratic & Inverse Relationships

Explore how we tell when two variables are in quadratic or inverse relationships in this lesson. Once you understand the basics, we'll go over a couple of examples where these relationships show up in a physics class.

### 11. Inverses of Cube Root Functions

A function gives us a y-value for a specific x-value. If the y-value is used in an inverse function, we obtain the original x value. In this lesson, we explore the general meaning of inverse functions and show how to find the inverse of cube root functions.

### 12. Quadratic Models: Inverse & Vertex Form

In a data set for age vs. Body Mass Index, we can find a quadratic regression model to fit the data using a TI-84 graphing calculator. Then we will convert this function into vertex form, view its graph and find its inverse, if one exists.

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### Other Chapters

Other chapters within the Explorations in Core Math - Algebra 2: Online Textbook Help course

- Explorations in Core Math Algebra 2 Chapter 1: Foundations for Functions
- Explorations in Core Math Algebra 2 Chapter 2: Quadratic Functions
- Explorations in Core Math Algebra 2 Chapter 3: Polynomial Functions
- Explorations in Core Math Algebra 2 Chapter 4: Exponential and Logarithmic Functions
- Explorations in Core Math Algebra 2 Chapter 5: Rational and Radical Functions
- Explorations in Core Math Algebra 2 Chapter 7: Probability
- Explorations in Core Math Algebra 2 Chapter 8: Data Analysis and Statistics
- Explorations in Core Math Algebra 2 Chapter 9: Sequences and Series
- Explorations in Core Math Algebra 2 Chapter 10: Trigonometric Functions
- Explorations in Core Math Algebra 2 Chapter 11: Trigonometric Graphs and Identities
- Explorations in Core Math Algebra 2 Chapter 12: Conic Sections