To Infinity... And Beyond Chris Harrow

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.

Exponential Growth & Decay Graph

Logistic Functions Graph

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

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

Identities via Transformations Graph

Secant Graph

Ceilings & Floors

Bending the Center

Hyperbolic Trig Graph

Going Polar Graph Center Ceiling Floor

Just for fun Graph