Intermediate+Value+Theorem

=__The Intermediate Value Theorem__= We now know how to determine whether or not a function is continuous on a given interval. One important property of these continuous fuctions is that of Intermediate values: a continuous function that takes on two values must take all values in between.

In other words:

The Intermediate Value Theorem for Continuous Functions
Any function y=f(x) that is continuous on a closed interval [a,b] takes on every value between f(a) and f(b). For any value, y between f(a) and f(b), there must be some value c for which f(c)=y.