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DrDelMath

College Algebra
by Miller
SUMMARY

Chapter 2:   Functions and Graphs

Section 2.1: Cartesian Coordinate System

Coordinate Plane

Embedded in the following diagram are some obvious facts about the Cartesian Coordinate system, points in the system, and the Real Number coordinates of those points. Because these facts are obvious, the beginning student has a tendency to overlook them at times when their application might be appropriate. You are advised to study these facts and look for applications.
coordinate System

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The following two links provide useful insight into the distance formula.
The Distance Formula at PurpleMath distance formula link
The Distance Formula distance formula link

The following link provides a number of examples of the midpoint formula in action.
The Midpoint Formula at PurpleMath distance formula link
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Minimal List of Exercises Page 203.

If you understand the previous material you should be able to answer the following questions.
Each of these questions should be answered. Most of these questions are included in the MyMathLab homework requirement. If a particular concept is difficult for you, you should study the related text material and then try to answer some additional questions from the list provided by the department. In each case you are expected to make an honest adult evaluation of your understanding of the concept. Your ability to answer these questions is one tool to help you make that evaluation.
Section 2.1 Exercise Set: 1 - 8, 9, 11, 13, 17, 19.

 

Section 2.2: Circles

Formulas

Minimal List of Exercises Page 212.

If you understand the previous material you should be able to answer the following questions.
Each of these questions should be answered. Most of these questions are included in the MyMathLab homework requirement. If a particular concept is difficult for you, you should study the related text material and then try to answer some additional questions from the list provided by the department. In each case you are expected to make an honest adult evaluation of your understanding of the concept. Your ability to answer these questions is one tool to help you make that evaluation.
Section 2.2 Exercise Set: 1 - 14, 15, 17, 19, 20, 21, 22, 23, 25, 26, 30, 31, 37, 39, 41, 43, 45,47, .

Section 2.3: Definition of Function

Function: Definition and Notation

Picture of a Function

 

 

Function Notation

 

 

 

 

Picture of Function Notation

 

 

You should study the examples in the following Power Point presentation before proceeding
Introduction to Functions

 

Function: Graph

You should study the examples of several different types of functions as presented in the following Special Topic article.
Functions - Introductory Examples

Minimal List of Exercises Page 222.

If you understand the previous material you should be able to answer the following questions.
Each of these questions should be answered. Most of these questions are included in the MyMathLab homework requirement. If a particular concept is difficult for you, you should study the related text material and then try to answer some additional questions from the list provided by the department. In each case you are expected to make an honest adult evaluation of your understanding of the concept. Your ability to answer these questions is one tool to help you make that evaluation.
Section 2.3 Exercise Set: 3, 5, 9 - 14, 21 - 36.

 

Sections 2.4& 2.5: Linear Equations in Two Variables and Linear Functions and Some Applications

Review the fundamental information about linear equations in two variables HERE.

Function: Linear

Everything you could possibly want to know about linear functions. HERE

You should study Pages 14 - 17 of this Essay.

Minimal List of Exercises Page 238 & 254.

If you understand the previous material you should be able to answer the following questions.
Each of these questions should be answered. Most of these questions are included in the MyMathLab homework requirement. If a particular concept is difficult for you, you should study the related text material and then try to answer some additional questions from the list provided by the department. In each case you are expected to make an honest adult evaluation of your understanding of the concept. Your ability to answer these questions is one tool to help you make that evaluation.
Section 2.4 Exercise Set (Use Function notation as much as possible): 1 - 38, 51 - 54, 51 - 56, 71, 73, 75, 77, 79,

Section 2.5 Exercise Set (Use Function notation as much as possible):1, 3, 5, 6, 7, 8, 9, 11, 13, 19, 20, 23, 24, 29, 31, 35, 37, 39,41, 43, 45, 47, 51, 53

 

Section 2.6: Transformation of Functions

A Library of Basic Functions and their Graphs

Function: Library Basic Functions

 
 
Graphs of Linear Functions
 
Graph of Squaring Function
Graph of Cubing Function
Graph of Quadratic Function   Graph of Quadratic Function


Graph of Quadratic Function     Graph of Quadratic Function


Graph of Quadratic Function     Graph of Quadratic Function
Graph of Square Root Function
 
 
Graph of Reciprocal Function
 
 
Graph of Exponential Function
Graph of Logarithmic Function
 
Graph of Greatest Integer Function

Function: Transformations

Vertical and Horizontal Translations distance formula link

Absolute Value Translations distance formula link

Absolute Value Translations with Opposite distance formula link

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Minimal List of Exercises Page 270.

If you understand the previous material you should be able to answer the following questions.
Each of these questions should be answered. Most of these questions are included in the MyMathLab homework requirement. If a particular concept is difficult for you, you should study the related text material and then try to answer some additional questions from the list provided by the department. In each case you are expected to make an honest adult evaluation of your understanding of the concept. Your ability to answer these questions is one tool to help you make that evaluation.
Section 2.5 Exercise Set: 17,19,23,27,53,55,59,65,67,69,81,83,85,87,95,97,141,142,143,144.

 

Section 2.7: Analyzing Graphs of Functions and Piecewise-Defined Functions

Section X.Y: Increasing and Decreasing Functions

Function: Increasing, Decreasing, Even, and Odd

Minimal List of Exercises Page 223.

If you understand the previous material you should be able to answer the following questions.
Each of these questions should be answered. Most of these questions are included in the MyMathLab homework requirement. If a particular concept is difficult for you, you should study the related text material and then try to answer some additional questions from the list provided by the department. In each case you are expected to make an honest adult evaluation of your understanding of the concept. Your ability to answer these questions is one tool to help you make that evaluation.
Section 2.2 Exercise Set: 1,3,33,35,37,39,41,43,45,47,49,51,53,55,57,63,73,75.

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Section 2.8: Algebra of Functions and Function Composition

Function: Combining

The following picture is essential to understanding composition of functions.

                               Picture of Composition of Functions

Composition of Absolute Value with Quadratic distance formula link

Minimal List of Exercises Page 279.

If you understand the previous material you should be able to answer the following questions.
Each of these questions should be answered. Most of these questions are included in the MyMathLab homework requirement. If a particular concept is difficult for you, you should study the related text material and then try to answer some additional questions from the list provided by the department. In each case you are expected to make an honest adult evaluation of your understanding of the concept. Your ability to answer these questions is one tool to help you make that evaluation.
Section 2.6 Exercise Set: 1,3,5,7,9,11,13,15,17,19,21,23,27,31,33,37,39,43,47,49,51,53,55,57,59,561, 63,65,67,69,71,101,112,113,114,115.