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DrDelMath

College Algebra
by Blitzer
SUMMARY

Chapter 2:   Functions and Graphs

Section 2.0: Cartesian Coordinate System (page 90) Prerequiste Review for Chapter 2

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 97.

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 1.1 Exercise Set: 9, 10, 11, 17, 20.

Section 2.1: Definition of Function (page 198)

Function: Definition and Notation

Picture of a Function

 

 

Function Notation

 

 

 

 

Picture of Function Notation

 

 

Function Notation Exercises and Solutions

Sample Exercises

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

 

Function: Graph

Sample Exercises

Sample Exercises

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 210.

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: 27,29,37,71-76, 77,78,79,81,83,91.

Section 2.1a:  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

 

Section 2.2: 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.

 

Sections 2.3 & 2.4: Linear Functions and Slope

Function: Linear

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

Sample Exercises

You should study Pages 14 - 17 of this Essay.

Minimal List of Exercises Page 239 & 250.

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 (Use Function notation as much as possible): 1,5,9,11,15,25,27,29,35,37,39, 41,43,45,47,59,61,63,65,67.69,71

Section 2.4 Exercise Set (Use Function notation as much as possible).: 5 - 9, 15, 17, 21,24

 

Section 2.4a: Quadratic Functions

Function: Quadratic

Sample Exercises     Exercises about Quadratic Functions     Solutions to Exercises about Quadratic Functions

Minimal List of Exercises Page 152, 324, and 391.

These exercises are chosen to practice every form of analysis related to quadratic functions, quadratic equations and inequalitites in both one and two variables. You are expected to following the instructions in the text and then proceed to as much analysis as possible in each case. Use functions, function notation, definition of graph and sketches or computer generated graphs to perform the analysis.

Page 152 Exercise Set: 1 - 12, 65 - 82.

Page 324 Exercise Set: 5 - 8, 13 - 16, 27 - 38, 45 - 48.

Page 391 Exercise Set: 1 - 28.

 

Section 2.5: Transformation of Functions

Function: Transformations

Vertical and Horizontal Translations distance formula link

Absolute Value Translations distance formula link

Absolute Value Translations with Opposite distance formula link

Minimal List of Exercises Page 266.

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 2.6: Combining Functions

Function: Combining

The following picture is essential to understanding composition of functions.

                               Picture of Composition of Functions

Sample Exercises     Exercises about Factoring Relative to Composition

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.

 

Section 2.7: Inverses of Functions

Function: Inverses

The following diagram illustrates the relationship between a function and it inverse.
Think of the red arrows as the rule for a function f and the blue arrows as the rule for its inverse f-1

 Picture of Inverse Functions

Sample Exercises

Minimal List of Exercises Page 290.

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 2.7 Exercise Set: 1,3,5,7,9,11,13,15,21,23,25,29-34.

 

Section 2.8: Formulas

Formulas

Sample Completing the Square Exercises

Minimal List of Exercises Page 300.

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 2.8 Exercise Set: 1,3,5,7,13,15,17,19,21,25,27,31,33,35,37,39,41-52,53,55,57,59,67,69,95,96,97.