Intermediate Value Property

  • Thread starter KF33
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Homework Statement


I need to show the attached function satisfies the Intermediate Value Property.

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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.
 

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  • #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.
 
  • #3
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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.
 
  • #4
SammyS
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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.
That's a single example, well, not even a complete example. Definitely not a proof.
 

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