Graphing Rationals before vacation

We had a fun day in Accelerated Algebra 2 and all the kids were working hard.  We are learning all about rational functions now.  I explained to them that as a teacher it can be challenging to come up with just the right problem to put on a quiz.  Maybe I want them to graph a rational function that has 2 asymptotes and a hole.  I need the equation to work out nicely, so I have to play with it a bit. 

I told them today they were going to be the teacher and create 4 rational functions to graph.  I had grand plans that we didn't get all the way through, but they did the meat of the lesson.  Originally I created a teacher answer key for them as the teacher to complete.  They had to write 4 rational equation in factored form and graph them on www.desmos.com/  Then, they had to write them in standard form, fill in all the properties, and sketch the graph - essentially, creating an answer key.  This was as far as we got and I collected them because I didn't want them to get lost over vacation. 

I intended for them to then write the standard form of each on a student form and trade with another student. They complete all 4 problems and give it back to their "teacher" who checks it with their answer key.  But, alas, no time.

However, the conversation was rich and wonderful.  Even I was learning and that is super for the day before vacation.  I originally asked them to create a rational function with 1 vertical asymptote, 1 horizontal asymptote, and 1 slant asymptote.  Ah, but you can't.  Why not?  It was a good thinking question.  There were more questions to come - what's the difference between a reciprocal equation and a rational equation?  How do I "create" a hole?  How do I know the x-intercepts? the range?  All good.  Next year, I hope to have 2 days to complete this and actually get to the student part.

Here is the lesson:  Graphing Rational Activity

Here is a picture of the class working hard: