Saturday, September 27, 2008

Piecewise Function Success

Every year as I teach piecewise functions in precalculus, there are students who get it and can successfully graph and understand them, but there are too many students that struggle. I've tried various things, but nothing with consistent success. Well. Last week after school I was helping a struggling student, and as I was looking over her old test, I saw that the mistake she seemed to make on the "3 piece" piecewise function was that to graph it, she made a big table with the same x values and used the same x values for all 3 pieces. I started to say what her mistake was, but then it struck me that if she reworked the idea, it could be very useful.

It worked for all the struggling students I had a chance to try it on, so I think this is how I'll start next year, and then show them the "other" way for those that "get it" and don't want to make such a big table.


  1. Ms. Cookie - That is fabulous, as usual! I haven't had to teach this at the high school level before, but I will soon, so I have been looking for a good way to do it - I think you found it!!

  2. Anonymous2:23 PM

    I really like this way too....I'm always amazed by how much kids struggle with this concept. I like this as a scaffold until they can really conceptualize what's happening.

  3. This is awesome!!! Thank you so much for sharing!!

  4. Anonymous10:55 AM

    Thanks for your kind words. I do think this will (hopefully) eradicate the what-goes-where and the pesky-boundary-forgetting issues they seem to struggle with.

    Ms. Cookie

  5. Anonymous12:28 PM

    WOW! That makes so much sense. I will be stealing, ahem, borrowing this idea as well.

    What an awesome way to get the point across about the function only existing in a partial domain.

    Thank you!

  6. I not only stole it, I powerpointed it.

  7. Unless I'm making a real big mistake, I think your values for the 3-(x-5)^2 column are wrong.

    x x-5 (x-5)^2 3-(x-5)^2
    4 -1 1 2
    5 0 0 3
    6 1 1 2
    7 2 4 -1

  8. Anonymous5:31 PM

    Ach! Thank you ... I changed the function to "move it to be nicer" and I forgot to fix the y values.

    Thanks Eagle Eye Bill.

    Ms. Cookie

  9. Anonymous12:53 PM

    Okay, stole it, powerpointed it, and used it in class today.

    Not one person at the end of class misunderstood what piecewise functions are.

    First time that has ever happened! What an awesome idea.
    Thank you!!

  10. What about graphing all three functions. then erasing the parts that you don't need?

  11. I love love love this! I ALWAYS have trouble getting my kids to understand graphing piecewise functions by hand and it creates a real problem for them when I get them again for calculus the next year! Thanks for sharing!

  12. Anonymous3:46 PM

    Hi I'm a student and I've been struggling with these for a while and I have a big test coming up with week, and I have a question. How do I know which boxes to shade out?

    1. Anonymous4:14 PM

      Look at the inequalities of the original problem. Shade out values that either are not on the boundary or are false for the inequality.