The greater the value of k, the closer the image of the direct proportional function is to the Y axis, and the closer the image of the inverse proportional function is to the X axis. In the proportional function, when k is greater than 0, the image passes through one or three quadrants, and y increases with the increase of x, so the greater the k value, the closer the image is to the y axis; In the inverse proportional function, when k is greater than 0, the image passes through one or three quadrants.

In each quadrant, y decreases with the increase of x, so the greater the value of k, the closer the image is to the x axis. 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 number set A, assume that the element in it is X, apply the corresponding rule F to the element X in A, and record it as f(x) to get another number set B, assume that the element in B is Y, and the equivalent relationship between Y and X can be expressed as y=f(x). The concept of a function includes three elements: the domain A, the domain B and the corresponding rule F, among which the core is the corresponding rule F, which is the essential feature of the function relationship.

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

Origin of function

The word "function" used in China's math book is translated. It was Li, an algebra expert in the 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". 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 "function" means that the formula contains 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 term equation refers to simultaneous linear equations with many unknowns, which are called linear equations.