# Chapter 1: Analyzing Functions

Difficulty Level:

**At Grade**Created by: CK-12

## Introduction

This section focuses on investigating functions both graphically and mathematically.

Lessons in this section specifically teach:

- Identifying the maximum and minimum values of a function both by investigating a graph and using Algebra.
- Identifying the rate of change of a function
- Understanding the concept of limit
- Recognizing and using asymptotes
- Understanding and using function notation
- Parent functions and the use of transformations
- Recognizing the difference between functions and relations
- Understanding the concept of intervals and the use of interval notation

By the time you finish this section, you should have a fresh understanding of what functions are, and how to manipulate them to find specific bits of information.

## Chapter Outline

- 1.1. Relations and Functions
- 1.2. Domain and Range
- 1.3. Intervals and Interval Notation
- 1.4. Average Rate of Change
- 1.5. Minimums and Maximums
- 1.6. Discrete and Continuous Functions
- 1.7. Increasing and Decreasing Functions
- 1.8. Limits and Asymptotes
- 1.9. Infinite and Non-Existent Limits
- 1.10. Linear and Absolute Value Function Families
- 1.11. Square and Cube Function Families
- 1.12. Vertical and Horizontal Transformations
- 1.13. Stretching and Reflecting Transformations
- 1.14. Combining Transformations
- 1.15. Operations on Functions
- 1.16. Composition of Functions
- 1.17. Linear and Quadratic Models
- 1.18. Cubic Models

### Chapter Summary

## Summary

The concepts in this section explore the identification, transformation, combination, and application of linear, quadratic, cubic, and non-standard functions.

Prerequisites should include:

- A solid understanding of arithmetic, pre-algebra, and manipulation of equations
- Exposure to graphing with the Cartesian coordinate system
- Familiarity with the concepts of infinity and absolute value

Helpful would be:

- A basic familiarity with the concept of functions and the use of a graphing calculator
- Previous exposure to graphing quadratic functions and shapes
- A basic understanding of interval notation

### Image Attributions

## Description

Topics in this chapter include: function minimums and maximums, increasing and decreasing functions, end behavior, function families, transformations, operations and compositions, and mathematical models.

## Difficulty Level:

At Grade## Tags:

## Subjects:

## Date Created:

Nov 01, 2012## Last Modified:

Feb 26, 2015
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