I gave my PreCalc kids what I call a “backwards” problem: I provided certain aspects of a function and then they were to try to find its equation. Kind of like Daily Desmos, but I gave them the verbal description of the function instead of the graph.
We did a few together and then I gave them a pretty hard one (had a slant asymptote in it). I gave them their homework and told them they could keep wrestling with the problem or they could start their homework. I figured most would start their homework. But, to my delight, throughout the hour several kids came up to me to ask, “Did I get it?!” Or, “Am I on the right track?”
I was so pleased that they found this interesting enough to give up homework time, but I was even more happy about the fact that I found problems that even teenage boys will wrestle with… 😉