Prompting Generalizations of Limits at Infinity

After my PreCalc students completed a rational functions packet (thanks largely to CME) I wanted to move directly into the study of limits. I started with the chart below which is pretty much exactly what JackieB shared. The difference was in the follow up; I didn’t want to scaffold their conclusions as much as she did. Which resulted in most students not understanding what I wanted for generalizations. Next time I need to reword that section, should I ask students what the possible values are for the limits first and then ask them to generalize how to know what the limit will be?  I also debated mixing up the order of the problems (as they are now the first three go to infinity, the next three go to a non-zero number and the remaining three go to zero) but hoped leaving them in order would highlight the pattern.  I try to avoid the “guess what the teacher’s thinking” game but also want to encourage them to make their own observations.  Solutions to my dilemma?

Original Post on Drawing on Math with a complete description of the unit.

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