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Homework Help: Function? Correspondence? Neither?

  1. Aug 30, 2010 #1
    1. The problem statement, all variables and given/known data

    Consider the following mathematical items. For each item, (1) indicate whether it has a natural interpretation as a function, a correspondence, or neither. If the item is a function or a correspondence, the indicate (2) its domain and range and (3) whether it is (a) real, (b) single-valued and (c) univariate.
    If the item is not a function, or is not real, single-valued or univariate, then justify your answer briefly.

    3. The attempt at a solution

    1. (1,1), (2,2), (3,3) is a function. Domain (1,2, 3), Range (1,2, 3) Single-valued?

    2. (1,1), (2,2), (1,3) is NOT a fuction. Domain (1,2), Range (1,2, 3) Single-valued

    3. (1,1), (2,1), (3,1) is a function. Domain (1,2, 3), Range (1) Single-valued

    4. (1,1), (2,(3,1)), (3,1) is a function. Domain (1,2, 3), Range (1, 3)-is it correct? Univariate

    5) ((1,1),2), ((2,1),3), ((2,1),4) is NOT a function. Domain (?), Range (2,3,4) Univariate

    Any mistakes?
     
  2. jcsd
  3. Aug 30, 2010 #2

    Office_Shredder

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    For number 4, what is f(2) supposed to be?
     
  4. Aug 30, 2010 #3
    Our teacher jumped into the material and barely covered it. So I still don't understand what (2,(3,1)) means.
     
  5. Aug 30, 2010 #4

    Office_Shredder

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    Ok. We are representing a function as a set of ordered pairs. The first entry is going to be x, and the second entry is going to be f(x).

    So for number 1, f(1)=1 since (1, 1) is in the set, f(2)=2 since (2,2) is in the set, f(3)=3 since (3,3) is in the set.

    For number 3, f(1)=1 since (1,1) is in the set; f(2)=1 since (2,1) is in the set and f(3)=1 since (3,1) is in the set
     
  6. Aug 30, 2010 #5
    Oh, this part, I understand.
    The one I am talking about (2,(3,1)) is correspondence, when one or more elements of domain are mapped to more than one element from the range. Typically, what is a range of this example?

    I am also struggling with whether it is (a) real, (b) single-valued and (c) univariate.
     
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