Finishing Up Polar Graphs

A long time ago at "math camp" (NCTM annual workshop), someone led a talk on how to relate the Limacons and Cartioids and Rose Petal Polar Graphs to the shifted or "squished" trig graphs in terms of y = f(x). This seemed to work out really well, and the students could visualize what happens in terms of the amplitude and the vertical shift. Anyway ... we're all done with that, and after exploring on the graphing calculator for the next day, this was their homework in precalculus:



Onwards and upwards to Logarithms which I subtitle (Drugs, Sex, & Rock n Roll) due to my first few examples which they figure out (and see why logs are useful): drug absorption/metabolization, population growth, & decibel levels and hearing loss.