Intermediate value theorem

In mathematical analysis, the intermediate value theorem states that if a continuous function, f, with an interval, , as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval. In mathematical analysis, the intermediate value theorem states that if a continuous function, f, with an interval, , as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval. This has two important corollaries: This captures an intuitive property of continuous functions: given f continuous on with the known values f(1) = 3 and f(2) = 5. Then the graph of y = f(x) must pass through the horizontal line y = 4 while x moves from 1 to 2. It represents the idea that the graph of a continuous function on a closed interval can be drawn without lifting a pencil from the paper.