The history of functional mathematics shows that the generation and development of important mathematical concepts play an inestimable role in the development of mathematics, and some important mathematical concepts play a fundamental role in the generation of mathematical branches. The function we just learned is a very important concept. Since Descartes introduced variables, concepts such as variables and functions have increasingly penetrated into various fields of science and technology. Observing the universe, operating celestial bodies, exploring heat conduction and revealing electromagnetic secrets are all closely related to the concept of function. It is in these practical processes that people deepen the concept of function. Looking back on the development history of the concept of function, it is impossible for junior high school students who are new to function to have a deep understanding, but it will undoubtedly help deepen their understanding of classroom knowledge and stimulate their interest in learning. The concept of function was first put forward. /kloc-Leibniz, a German mathematician in the 0/7th century, first used the word "turtle" to express power. For example, x, x2 and x3 are all called functions. Later, he used a function to represent the abscissa and ordinate of a point on a curve in a rectangular coordinate system. 17 18. Bernoulli, a student of Leibniz and a Swiss mathematician, defines a function as: "a quantity composed of a variable and an arbitrary constant." This means that any formula consisting of a variable X and a constant is called a function of X, and Bernoulli emphasized that functions should be expressed by formulas. Later, mathematicians felt that the concept of function should not be limited to formulas. As long as some variables change, others can also change accordingly. Whether the relationship between these two variables should be expressed by a formula is not the criterion for judging the function. 1755, the Swiss mathematician Euler defined a function as "if some variables depend on other variables in some way, that is, when the latter variable changes, the former variable also changes, so we call the former variable a function of the latter variable." In Euler's definition, it is not emphasized that functions should be expressed by formulas. At that time, some mathematicians were not used to expressing functions with formulas, and some mathematicians were even skeptical. They call functions that can be expressed by formulas "true functions" and functions that cannot be expressed by formulas "false functions". In 2008+082 1 year, French mathematician Cauchy gave a function definition similar to the current middle school textbook: "There is a certain relationship between some variables. Once the value of one variable is given, when other variables can be determined, the initial variable is called independent variable, and the other variables are called functions. In Cauchy's definition, the word independent variable first appeared. 1834, the Russian mathematician Lobachevsky further put forward the definition of function: "The function of x is such a number that it has a certain value for each x" and changes with x, and the function value can be given by an analytical formula or a condition, which provides a method for finding all corresponding values. This dependence of the function can exist, but it is still unknown. "This definition points out the necessity of the corresponding relationship (condition) and uses this relationship to find the corresponding value of each X. 1837 German mathematician Dirichlet thinks that how to establish the corresponding relationship between X and Y is irrelevant, so his definition is:" If there is always a completely certain value corresponding to each value of X, then Y is the function of X. " The variable y is called a function of x, and there is only one rule that makes every value in the range of this function have a definite Y value corresponding to it, no matter whether this rule is a formula, an image, a table or other forms. This definition is more biased than the previous definition, which provides convenience for theoretical research and practical application. So this definition has been used for a long time. Since the German mathematician Cantor's set theory was accepted by everyone, the concept of defining functions by set correspondence is now used in high school textbooks. The word "function" used in China's math book is translated. The book Algebra (1895) was translated by Li, an algebra expert in Qing Dynasty. Translate it into a function number? The word "Xin" and "Han" were commonly used in ancient China, both of which had the meaning of "Han". The definition given by Li is that "every formula contains days, which is a function of days." 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: "When a formula contains a variable X, the formula is called a function of X."