Proving Intermediate Value Property: Function Analysis

[KF33]

Homework Statement

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

Homework Equations

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.

 

[mathwonk]

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.

 

[KF33]

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.

 

[SammyS]

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.