The first thing I asked groups (visible random) to do was graph y = x and the reciprocal y = 1/x. When they were done I had them graph y = x^2 and the reciprocal y = 1/x^2.
Here is what it looks like.
Then we tried a specific quadratic and its reciprocal. This required students to factor the quadratic and find the vertex. Okay this was the first time we had mentioned or tried factoring a quadratic. They would also need the vertex. This proved more difficult than I had expected. No worries we will be factoring soon.
Then I asked students to graph y = sin x and its reciprocal y = 1/sin x = csc x.
Students were then asked to graph y = cos x and its reciprocal y = 1/cos x = sec x.
This group did both in one graph.
Lastly we looked at combining two functions to graph y = tan x = sin x / cos x. This is not an example of reciprocal functions but it is an example of a rational function. We used a table of values for sin x and cos x to create a table of values for sin x / cos x.
Lastly the nice thing about whiteboarding - you get to see students doodles. Layet Johnson an artist friend of mine would be proud.
Clearly not me -this guy has hair!