The symmetry center formula of the function is that f(x) is symmetric about (a, b), so there are f(x)+f(2a-x)=2b or f(a+x)+f(a-x)=2b}. Symmetry: a function: f(a+x)=f(b-x) holds, and f () is symmetric about the straight line x=(a+b)/2. F(a+x)+f(b-x)=c, and f(x) is symmetric about this point ((a+b)/2, c/2).

Images with two functions: y=f(a+x) and y=f(b-x) are symmetrical about the straight line x=(b-a)/2. Proof: Take a point (m, n) on the function and prove that the point after symmetric transformation is still on the function. As proved by the central symmetry formula, take a point (m, n) on the function and the symmetry point is (a+b-m, c-n). If fa+(b-m))+f(b-(b-m)=c, then f(a+(b-m))+n=c, that is to say, f(a+(b-m))=c-n, and the symmetry point is also on the function.

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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, and 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 equivalence relation between Y and X can be expressed as y=f(x). The concept of function consists of 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 "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.