# Geometric Properties of Graphs

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.

__Increasing, Decreasing and Constant Function__: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 .