Test 1

(Part 2: Take home)

I affirm that I have not discussed this exam with anyone and that all work is my own, done without assistance or input, direct or indirect.

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Signed

Please print this page, sign it, and submit it as the first page of your work.

If a problem asks you to create a GC document that does something, create the document, save it with your name and the problem number as the document's name (e.g., Pat-Test 1 Prob 3a), print it, and include the printout with your submitted work (in the proper order).

If a problem asks you to explain something, create a Word document, including any diagrams or illustrations (including GC graphs), title it with the problem number and your name, print it, and include the printout with your submitted work (in the proper order).

Consult the section of GC Help on graphing functions in three dimensions for questions about using Graphing Calculator.

Please note: If you have trouble printing, then please send your files (properly named) to me by email.

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Problem 1

  1. (20 points) Define a function parametrically that has a graph that looks like a knot in space, such as this:

  1. (20 points) If you were successful in making a graph similar to this one, then explain to someone else (in text) how to think about this graph so that he or she could re-create it or one similar to it.

    If you were unsuccessful in making a graph similar to this one, then explain your lack of success. Even if you were unsuccessful in making the graph, you can earn 85% of full credit by developing insight into your difficulty.

Problem 2

  1. (20 points) Show the projection into the x-y plane of the curve you created in Problem 1 (even if your curve failed to be a closed loop). Your solution to this one should work no matter the space curve you use it on.
    For example,

  1. (20 points) If you were successful in making a graph similar to this one, then explain to someone else (in text) how to think about this graph so that he or she could re-create it or one similar to it.

    2. If you were unsuccessful in making a graph similar to this one, then explain your lack of success. Even if you were unsuccessful in making the graph, you can earn 85% of full credit by developing insight into your difficulty.

Problem 3

  1. (20 points) Show that your space curve was made by evaluating some function along a path in the x-y plane, like this (double-click if the diagram is not animated):

  1. (20 points) If you were successful in making a graph similar to this one, then explain to someone else (in text) how to think about this graph so that he or she could re-create it or one similar to it.

    2. If you were unsuccessful in making a graph similar to this one, then explain your lack of success. Even if you were unsuccessful in making the graph, you can earn 85% of full credit by developing insight into your difficulty.