# 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

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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
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Date Created:

Nov 01, 2012
Last Modified:

Mar 23, 2016
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