17 May 2013

Guess the Function!

     I've been learning all about functions in math (they're really awesome!).  In my math book, Life of Fred (by Stanley F. Schmidt, Ph.D.), which is a wonderful and wacky math curriculum, the game "Guess the Function" frequently appears in the functions chapter.  I've decided to start doing "Guess the Function" on this blog.  I'm not sure how often I'll be able to do it, but I'll at least try to keep it up.

     Here's how it works:  I give examples of a function.  You then try to come up with a rule that fits all of the examples.  It doesn't actually have to be the one that I was thinking of, as long as it fits all the given examples.  If you come up with a function that works with the examples, you win!  All winners will be given imaginary laurel wreaths.
     Note:  If you actually do figure out the function I was thinking of, then you get an imaginary trophy. O.o

And for those of you who don't know what a function is:

     Here's the definition given by my math book:  A function is a rule which assigns to each element of the first set exactly one element of the second set.  (By the way, the first set is called the domain and the second set is called the codomain.)  Let me give an example:  Okay, so the first set (the domain) is the 13 dwarves in The Hobbit.  The second set (the codomain) is the alphabet.  If I assigned all dwarves whose names contained less than five letters to D and all the other dwarves (the ones whose names contained five or more letters) to L, that would be a function.  So according to this function, Kili would be assigned to D and Bombur would be assigned to L.  Does that make sense?  (I hope it does; if not, please tell me in a comment and I'll do my best to explain it better.)  Okay, here we go!

The domain is the set of all men who signed the United States Declaration of Independence.  The codomain is the colours in a Crayola 8-pack set of crayons.

Robert Treat Paine  ----------------------------->  Red
John Penn  ---------------------------------------->  Green
Thomas Jefferson  ------------------------------->  Green
William Hooper  --------------------------------->  Orange
George Wythe  ----------------------------------->  Red
Josiah Bartlett  ------------------------------------>  Green
George Walton  ---------------------------------->  Orange
Button Gwinnett  -------------------------------->  Green

Please leave a comment with your function for this example!

14 comments:

  1. I don't really understand, but that's probably because I'm still in Algebra. :P

    *googles functions*

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    1. Can you give an example of what a function would look like with your Hobbit example?

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    2. Thorin ---> L
      Kili ---> D
      Fili ---> D
      Balin ---> L
      Dwalin ---> L
      Oin ---> D
      Gloin ---> L
      Dori ---> D
      Nori ---> D
      Ori ---> D
      Bifur ---> L
      Bofur ---> L
      Bombur ---> L

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    3. I'm still in Algebra (Algebra 2) as well, Hyper. Well, it appears an example has already been given...(thanks, Jag!) Does that make it easier to understand, or is it still unclear?

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    4. I get how it works...sort of. But isn't what Jag just gave the same thing you gave in your post? (Thorin ---> L vs. John Penn ---> Green) What's the answer you want us to give?

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    5. I'm sorry, I guess I didn't understand your question...I get it now! Okay, so in the Hobbit example, the answer would look like this: Assign all dwarves whose names contain less than five letters to D and all other dwarves to L. Sorry for the misunderstanding!

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  2. I thought that the second set was the range, not the codomain... at least my maths book says it is :P

    I'll try to work it out, but no promises... I'll probably go way off into some complicated formula :P

    ReplyDelete
    Replies
    1. The difference between range and codomain is this: the codomain is the entirety of the second set. You can have a codomain where not every element is 'hit' by something in the domain. But the range is every element in the second set that is 'hit' by something in the first set. E.g., in the Hobbit example, the codomain is the alphabet, but the range is {D,L}. (In a 1-1 function, the range is equal to the codomain. Maybe that's what your math book is referring to.)

      Hint: this one isn't very complicated. I wanted it to be guessable. (But I do so love coming up with unguessable functions... ;) )

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  3. Ah! Math! *runs from blog post and hides* Thank goodness I'm done with math for a while. I don't have to do any until Autumn! *throws confetti in the air* And I don't think I've gotten into functions yet...I'm starting Algebra 2 next semester.

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  4. XD Yay! No more math! :D Usually I dislike it, too, but for some reason I really like functions.

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    1. Huh. Well I'm glad there's something that makes it interesting for you! :)

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  5. Functions!! Maths!!! BIG PANIC!

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  6. This comment has been removed by the author.

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  7. Here's what I came up with

    If the last name contains double letters assign to Green

    If the last name ends with "e" then assign to Red

    If the last name follows neither function then assign to Orange
    :)

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