Unit 1: Analytic Geometry Most of the material in this unit will be review. However, the notions of points, lines, circles, distance, and functions will be central in everything that follows. Lines are basic geometric objects which will be of great importance in the study of differential calculus in the study of tangent lines and linear approximations.
We will also take a look at the practical uses of mathematical functions. This course will use mathematical models, or structures, that predict practical situations in order to describe and study a number of real-life problems and situations. They are essential to the development of every major business and every scientific field in the modern world.
Unit 1 Time Advisory
This unit should take you approximately 9.5 hours to complete.
☐ Subunit 1.1: 2.5 hours
☐ Subunit 1.2: 2 hours
☐ Subunit 1.3: 3 hours
☐ Subunit 1.4: 2 hours
Unit1 Learning Outcomes
Upon successful completion of this unit, the student will be able to:
- Create and analyze graphs of points, lines, and circles in a plane.
- Define and identify the domain, range, and graph of a function.
- Define and identify one-to-one, onto, and linear functions.
- Analyze and graph transformations of functions, such as shifts and
dilations.
1.1 Lines
- Reading: Whitman College: David Guichard’s Calculus: Chapter 1:
Analytic Geometry: “Section 1.1: Lines”
Link: Whitman College: David Guichard’s Calculus: Chapter 1:
Analytic Geometry: “Section 1.1:
Lines” (PDF)
Instructions: Please click on the link above and read Section 1.1
(pages 14-17) in its entirety. Working with lines should be
familiar to you, and this section serves as a review of the notions
of points, lines, slope, intercepts, and graphing.
This reading should take you approximately 30 minutes to
complete.
Terms of Use: This resource is licensed under a Creative Commons
Attribution-NonCommercial-ShareAlike
License. This
text was originally written by Professor David Guichard. It has
since been modified to include edited material from Neal Koblitz of
the University of Washington, H. Jerome Keisler of the University of
Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can
access the original version
here.
Assignment: Whitman College: David Guichard’s Calculus: Chapter 1: Analytic Geometry: “Exercises 1.1: Problems 1-18” Link: Whitman College: David Guichard’s Calculus: Chapter 1: Analytic Geometry: “Exercises 1.1: Problems 1–18” (PDF)
Instructions: Please click on the above link and work through problems 1-18. When you are done, check your answers against “Appendix A: Answers”.
Completing this assignment should take you about two hours to complete.Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here.
1.2 Distance between Two Points, Circles
- Reading: Whitman College: David Guichard’s Calculus: Chapter 1:
Analytic Geometry: “Section 1.2: Distance Between Two Points;
Circles”
Link: Whitman College: David Guichard’s Calculus: Chapter 1:
Analytic Geometry: “Section 1.2: Distance Between Two Points;
Circles” (PDF)
Instructions: Please click on the link above and read Section 1.2
(pages 19 and 20) in its entirety. This reading reviews the notions
of distance in the plane and the equations and graphs of circles.
This reading should take approximately 30 minutes to complete.
Terms of Use: This resource is licensed under a Creative Commons
Attribution-NonCommercial-ShareAlike
License. This
text was originally written by Professor David Guichard. It has
since been modified to include edited material from Neal Koblitz of
the University of Washington, H. Jerome Keisler of the University of
Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can
access the original version
here.
Assignment: Whitman College: David Guichard’s Calculus: Chapter 1: Analytic Geometry: “Exercises 1.2: Problems 1, 2, 6” Link: Whitman College: David Guichard’s Calculus: Chapter 1: Analytic Geometry: “Exercises 1.2: Problems 1, 2, 6” (PDF)
Instructions: Please click on the above link and work through problems 1, 2, and 6 in Exercises 1.2. When you are done, to check your answers against “Appendix A: Answers”.
This assignment should take you approximately 30 minutes to complete.
Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here.Assignment: Temple University: Gerardo Mendoza and Dan Reich’s Calculus on the Web: Calculus Book I: Marc Renault and Molly M. Cow’s “Distance” Module and Dan Reich’s “Equations of Circles II” Module Link: Temple University: Gerardo Mendoza and Dan Reich’s Calculus on the Web: Calculus Book I: Marc Renault and Molly M. Cow’s “Distance” Module and Dan Reich’s “Equations of Circles II” Module
Instructions: Please click on the link above and click on the number 5 next to “Distance” to launch the first module and complete problems 1-5. Then return to the index and click on the number 8 next to “Circles II” to launch the second module and complete problems 1-5. If at any time the problem set becomes too easy for you, feel free to move forward.
Completing this assignment should take you approximately one hour to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.3 Functions
- Reading: Whitman College: David Guichard’s Calculus: Chapter 1:
Analytic Geometry: “Section 1.3: Functions”
Link: Whitman College: David Guichard’s Calculus: Chapter 1:
Analytic Geometry: “Section 1.3:
Functions” (PDF)
Instructions: Please click on the link above and read Section 1.3
(pages 20-24) in its entirety. This reading reviews the notion of
functions, linear functions, domain, range, and dependent and
independent variables.
This reading should take you approximately one hour to complete.
Terms of Use: This resource is licensed under a Creative Commons
Attribution-NonCommercial-ShareAlike
License. This
text was originally written by Professor David Guichard. It has
since been modified to include edited material from Neal Koblitz of
the University of Washington, H. Jerome Keisler of the University of
Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can
access the original version
here.
Assignment: Whitman College: David Guichard’s Calculus: Chapter 1: Analytic Geometry: “Exercises 1.3: Problems 1-16” Link: Whitman College: David Guichard’s Calculus: Chapter 1: Analytic Geometry: “Exercises 1.3: Problems 1-16” (PDF)
Instructions: Please click on the link above and work through problems 1-16. When you are done, check your answers against “Appendix A: Answers”.
This assignment should take you approximately two hours to complete.Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here.
1.4 Shifts and Dilations
- Reading: Whitman College: David Guichard’s Calculus: Chapter 1:
Analytic Geometry: “Section 1.4: Shifts and Dilations”
Link: Whitman College: David Guichard’s Calculus: Chapter 1:
Analytic Geometry: “Section 1.4: Shifts and
Dilations” (PDF)
Instructions: Please click on the link above and read Section 1.4
(pages 25-28) in its entirety. This reading will review graph
transformations associated with some basic ways of manipulating
functions like like shifts and dilations.
This reading should take you approximately 30 minutes to
complete.
Terms of Use: This resource is licensed under a Creative Commons
Attribution-NonCommercial-ShareAlike 3.0
License. This
text was originally written by Professor David Guichard. It has
since been modified to include edited material from Neal Koblitz of
the University of Washington, H. Jerome Keisler of the University of
Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can
access the original version
here.
- Assignment: Temple University: Gerardo Mendoza and Dan Reich’s
Calculus on the Web: Calculus Book I: Lavanya Myneni and Molly M.
Cow’s “Recognizing Algebraic Functions” Module
Link: Temple University: Gerardo Mendoza and Dan Reich’s Calculus
on the Web: Calculus Book I:
Lavanya Myneni and Molly M. Cow’s “Recognizing Algebraic Functions”
Module
Instructions: Please click on the link above and select the “Index” button. Click on the number 18 next to “Transforming Graphs” to launch the module and complete problems 1-15. If at any time the problem set becomes too easy for you, feel free to move forward.
This assignment should take you approximately an hour and 30 minutes to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.