Assignment #2

The Intermediate Value Theorem says that a function must be continuous over a given interval. If f(x) (a function) is continuous over a given interval, then there is a value of that function, such as x, that lies within that interval as well. It is quite important to establish that the function is continuous because, otherwise, it will have holes, jumps, gaps, etc. This theorem is considered an existence theorem because it implies that a number exists but it does not give us the exact number.