The monotonicity of a function is also called the increase or decrease of a function. Monotonicity of a function is a local concept of an interval.

Increasing function and decreasing function

Generally speaking, let the domain of the function f(x) be I: if the values of any two independent variables belonging to an interval in I are x 1 and x2, then when X 1 < X2, there will be F (X 1) < F (X2). Then let's assume that f(x) is increasing function in this interval.

On the other hand, when X 1 < X2, if the values of any two independent variables belonging to an interval in I are F (x 1) > F (x2), then F (x) is a decreasing function in this interval.