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Intermediate Value Property

  1. Jun 23, 2016 #1

    KF33

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    1. The problem statement, all variables and given/known data
    I need to show the attached function satisfies the Intermediate Value Property.

    2. Relevant equations


    3. The attempt at a solution
    I looked at the property definition, but I am really unsure what is being stated. I think if I knew what the property was stating, I could do the problem.
     

    Attached Files:

    KF33, Jun 23, 2016
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  3. Jun 23, 2016 #2

    mathwonk

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    a function has the IV property if the image of every interval is an interval. i.e. if for every interval [x1,x2] in the domain, the set of values f(x), for all x with x1 ≤ x ≤ x2, is also an interval.
     
    mathwonk, Jun 23, 2016
  4. Jun 23, 2016 #3

    KF33

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    Is it enough to say an interval could be [-10,0]. Then I select x1 to be -9 and x2 to be -1. f(x1)=-.412 and f(x2)=-.841. I look and select k to be between those and find a c value which f(c)=k.
     
    KF33, Jun 23, 2016
  5. Jun 23, 2016 #4

    SammyS

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    That's a single example, well, not even a complete example. Definitely not a proof.
     
    SammyS, Jun 23, 2016
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