This activity is a hands on activity where students create the Cycloid Curve, the Prolate Cycloid Curve, and the Curtate Cycloid Curve. Creating all three curves on the same piece of paper allows the students an opportunity to compare and contract the three curves. This activity would be used as an enrichment activity for a pre-calculus class that is examining functions.
Identify the effect on the graph of replacing 𝘧(𝘹) by 𝘧(𝘹) + 𝘬, 𝘬 𝘧(𝘹), 𝘧(𝘬𝘹), and 𝘧(𝘹 + 𝘬) for specific values of 𝘬 (both positive and negative); find the value of 𝘬 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.