This is best BEFORE teaching how to find asymptotes and graph rational functions.
Start with just a 5 minute introduction to what an asymptote means and what it looks like. Then, the kids jump into Investigation 1.
The kids analyze the factored forms of the functions and figure out what is causing the vertical asymptotes and holes.
Then, the second investigation follows with horizontal and slant asymptotes.
For this one, I made a little reference "cheat sheet" for the students. If they do not recognize what is happening on the calculator screen, they can take a peek at these samples.
For both parts of this activity, it works best if you have the students cut the cards apart. This way, they can separate and differentiate them. Then, they can look at each "collection" and start to hunt for the patterns and characteristics of each feature.
I like to have the kids work in pairs.
Click here to download all the files for the "What Makes an Asymptote" Investigation lesson.
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