Question 1
What does the Intermediate Value Theorem say about a function $f$ that is continuous on $[a,b]$?
Question 2
Suppose $f$ is continuous on $[1,4]$, $f(1)=-2$, and $f(4)=5$. Which conclusion is guaranteed by the Intermediate Value Theorem?
Question 3
Why is continuity needed in the Intermediate Value Theorem?
Question 4
A continuous function $f$ satisfies $f(2)=-1$ and $f(6)=3$. Which statement must be true?
Question 5
A continuous function has $f(0)=4$ and $f(5)=-2$. Which value is guaranteed to be reached by the function on $[0,5]$?
