What Makes an Asymptote? Guided Inquiry with Rational Functions

As you probably know by now, I love inquiry-based lessons.

Here is one of my favorites --- I decided to try a different approach to teaching rational functions.

Instead of outlining the whole procedure for finding the domain, vertical asymptotes, horizontal asymptotes, etc., I twisted the lesson into an investigation.

The kids figure out for themselves what parts of the rational function cause certain features in the graph.

This process helps them understand the different types of asymptotes a lot better, and they remember what causes each one more easily.

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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Have your kids played the "Simplifying Rational Expressions Golf Game" yet?  It is a perfect review of factoring within rational expressions to lead into this lesson (or just for fun!)  - Check it out in my TPT store.

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