End Behavior of Rational Functions

This is the activity I used a couple of months ago to help students investigate the end behavior of rational functions.

The second part of the activity (not shown) asks them complete three statements:

  1. If the degree of the numerator is greater than the degree of the denominator, then…
  2. If the degree of the numerator is equal to the degree of the denominator, then…
  3. If the degree of the numerator is less than the degree of the denominator, then …

I thought it worked rather well to help them understand why the three different cases occur. We were able to have great conversations about rates of growth. “Weird stuff happens in the middle, but in the long run, the bottom gets bigger faster, so the function goes to zero.”.  I like this approach much better than presenting the “rules” for the three cases and just asking them to use them.

The students conjectures were not a precisely worded as I would have liked. I think that when I use this next year, I’ll still include the conjectures in Part II. However I’m thinking of changing/adding another part that we’ll complete as a whole class where we formalize the wording together.

Any suggestions for improvement would be greatly appreciated!

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5 Responses to End Behavior of Rational Functions

  1. John Golden says:

    I wonder if an extra instruction about “Use scientific notation to record 2 significant digits of these functions values as the input becomes large in magnitude.” And I’d like to ask some kind of “What do you notice?” before they get to the conditional statements on the back.

  2. Adam P. says:

    I really like the way you’ve organized the table….the way they do the grey columns after looking at the other values is really beneficial!

  3. Really excellent visual appeal , I’d value it 10 out of 10.

  4. Alyssa Jane says:

    The table looks great! It is a great way to organize the information for comparison! I do think it will be able to generate some valuable conversation about what is going on!

  5. Pingback: Prompting Generalizations of Limits at Infinity | Productive Struggle

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