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?

It means that for every value $\,c\in [f(-3),f(6)]=[-2,3]\,$ there exists at least one value $\,x_c\in [-3,6]\,$ s.t. $\,f(x_c)=c\,$.
The above, for example, tells us the function has a zero in $\,[-3,6]\,$...
