y = 1/x

What a nice way to end the year! My Algebra II/Precalc group, coming off conic sections, were confronted with this. I asked them to create a table, and hand-graph. Lots of reasonably interesting discussion about getting more data points, then about the discontinuity and asymptote (first time they have run into a vertical one), and that horizontal asymptote. We digressed to talk about point discontinuities (eg, ), and then I got a moment of satisfaction.

. Someone knew it was a vertical shift.

. Someone guessed it was a horizontal shift. Verified.

. Guess: vertical stretch. Verified.

Someone asked about a horizontal stretch. We looked at and to get the relationship.

And then didn’t really bother anyone. Someone started dividing right away.

Transforming functions? Taught so much earlier? It sunk in.