1. To Infinity... And Beyond Chris Harrow chrish@westminster.net http://casmusings.wordpress.com chrish@westminster.net http://casmusings.wordpress.com

2. To Infinity... And Beyond This workshop applies the reciprocal transformation to various function families. It offers an innovative understanding of several pre-calculus topics (including exponential, logistic, rational and trigonometric functions), unifying several families through a handful of underlying mathematical structures. Participants will discover that many historically complicated problems and concepts are both richer and greatly simplified in this process. The session concludes with a novel investigation of polar functions.

3. Exponential Growth & Decay Graph

5. Logistic Functions Graph

7. Spreading Disease Assume 30 people in a class. Assign each person a number Let each store a 5-6 digit number in randseed Run randint(1,30,#) # sick over time is logistic; there is a ceiling

8. AV & SQ Remember What’s invariant under SQ? How do the others change?

9. Identities via Transformations Graph

11. Secant Graph

13. Ceilings & Floors

16. Bending the Center

18. Hyperbolic Trig Graph

20. Going Polar Graph Center Ceiling Floor

22. Just for fun Graph