The definition of function monotonicity is one of the important properties of a function. It describes the changing trend of the function within a certain interval.
Specifically, if a function is in a certain interval, for any x1, x2 (x1 Function (function), mathematical term. Its definition is usually divided into traditional definition and modern definition. The essence of the two definitions of function is the same, but the starting point of describing the concept is different. The traditional definition starts from the perspective of motion change, while the modern definition starts from the perspective of collection and mapping. The modern definition of a function is to give a number set A, assuming that the element in it is x, and apply the corresponding rule f to the element x in A, denoted as f(x), to obtain another number set B , assuming that the element in B is y, the equivalent relationship between y and x can be expressed as y=f(x). The function concept contains three elements: definition domain A, value range B and corresponding rule f. Function was first translated by Li Shanlan, a mathematician from the Qing Dynasty in China, from his book "Algebra". The reason why he translated it this way is that "any variable that is a function of another variable is a function of that variable." That is to say, a function refers to a quantity that changes as another quantity changes, or in other words, a quantity changes with the change of another quantity. Contains another quantity. Function representation method: The method of using equations containing mathematical relationships to express the functional relationship between two variables is called the analytical expression method. The advantage of this method is that it can express the quantitative relationship between the function and the independent variable concisely, accurately and clearly; the disadvantage is that it often requires more complex operations to find the corresponding value, and some functional relationships in actual problems are not necessarily can be expressed using expressions. The method of using a list to express the functional relationship between two variables is called the list method. The advantage of this method is that the corresponding function values ??can be directly read from the values ??of the known independent variables in the table; the disadvantage is that only part of the corresponding values ??can be listed, making it difficult to reflect the full picture of the function.