Intermediate Value Theorem guarantee I'm doing a review packet for Calculus and I'm not really sure what it is asking for the answer?
The question is:
 Let f be a continuous function on the closed interval [-3, 6].  If f(-3)=-2 and f(6)=3, what does the Intermediate Value Theorem guarantee?
I get that the intermediate value theorem basically means but not really sure how to explain it?

The actual statement of the Intermediate Value Theorem is as follows.
Let $f$ be a continuous function on the closed interval $[a,b].$ Then for any $c \in (f(a),f(b))$ (this is an open interval), there exists $x \in (a,b)$ such that $f(x) = c.$
In your case, it guarantees the existence of a zero in the interval $[-3,6].$
Something interesting to note is that if $f$ is differentiable on $[a,b],$ then $f^{\prime}$ has the intermediate value property. This is known as Darboux's Theorem and is a nice exercise.
