The graph in Figure 1 (a) is always rising as we move to the right, a geometric indication that the function is increasing; that is, as increases, so does the value . On the other hand, the graph in Figure 1 (b) is always falling as we move to the right, indicating that the function g is decreasing; that is, as increases, the value of decreases. In Figure 1 (c), the graph doesn’t rise or fall, indicating that h is a constant function whose values do not change as we increase . The following definition makes these ideas more precise.
Let the interval be contained in the domain of the function .
(i) is increasing on if for every two numbers and in with we have .
(ii) is decreasing on if for every two numbers and in with we have .
(iii) is constant on if for every two numbers and in we have .