The field is non-negative; The range is the real number set r; The image of logarithmic function passes through a fixed point (1.0); When the radix is greater than 1, it has a monotonically increasing function in the definition domain, and when the radix is greater than 0 and less than 1, it has a monotonically decreasing function in the definition domain.

Function introduction:

Function, a mathematical term. Its definition is usually divided into traditional definition and modern definition. The essence of these two functional definitions is the same, but the starting point of narrative concept is different. The traditional definition is from the perspective of movement change, and the modern definition is from the perspective of set and mapping. The modern definition of a function is to give a set of numbers a, in which the elements are assumed to be X.

Apply the corresponding rule F to the element X in A, and record it as f(x) to get 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 concept of function includes three elements: domain A, range B and corresponding rule F, among which the core is corresponding rule F, which is the essential feature of function relationship.

Function was originally translated by Li, a mathematician of Qing Dynasty in China, in his book Algebra. He translated this way because any variable in this variable is a function of that variable, that is, a function means that one quantity changes with another quantity, or one quantity contains another quantity.

Source of function:

The word "function" used in China's math book is translated. It was Li, an algebra expert in China's Qing Dynasty, who translated "function" into "function" when he translated the book Algebra 1859. In ancient China, the word "Xin" and the word "Han" were universal and both had the meaning of "Han".

Li's definition is: "every formula contains heaven, which is a function of heaven." In ancient China, four words were used to represent four different unknowns or variables: heaven, earth, people and things. The meaning of this definition is: "Whenever a formula contains a variable X, the formula is called a function of X", so a function is a formula containing a variable.

The exact definition of an equation refers to an equation containing unknowns. However, in the early mathematical monograph "Nine Chapters Arithmetic" in China, the word "equation" means simultaneous linear equations with many unknowns, which are called linear equations.