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 $[0,2]$, with $f(0)=-1$ and $f(2)=3$. What does the Intermediate Value Theorem guarantee?
Question 3
Which condition is essential before the Intermediate Value Theorem can be applied?
Question 4
If $f$ is continuous on $[1,4]$, with $f(1)=2$ and $f(4)=8$, which value must $f$ take at some point in $[1,4]$?
Question 5
Which statement is a direct consequence of the Intermediate Value Theorem?
