The changes are:

f(a+x)=f(a-x)

f(x)=f(a-x)

f(-x)=f(b+x)

f(a+x)=f(b-x)

In this way, if there are symbols like x and -x, there is an axis of symmetry.

2. The basic expression of symmetric center: f(x)+f(-x)=0 is a odd function with symmetric center.

The basic changes are similar to the above. Just pay attention to the position of the equation.

3. Basic expression of periodic function: f(x)=f(x+t)

The variation is f(x+a)=f(x+b).

Pay attention to the position of symbols and equations.

4. Others, the above is just the foundation. There are many more complicated variants, but they will not be tested in the college entrance examination, so they will not be introduced.

The above three kinds are mainly to see the structure of the basic formula clearly, and then we can roughly distinguish the variant formula.

For example:

F(x+ 1)+f(x+2)=f(x+3) is a periodic function, and 3 is one of the periods.

Extended data:

Definition of function: Given a number set A, let the element in it be X, and now 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). We call this relationship a functional relationship, or function for short. The concept of function includes three elements: definition field A, value field C and corresponding rule F, among which the core is corresponding rule F, which is the essential feature of function relationship.

First of all, we should understand that a function is the corresponding relationship between sets. Then, we should understand that there is more than one functional relationship between A and B, and finally, we should focus on understanding the three elements of the function.

The corresponding rules of functions are usually expressed by analytical expressions, but a large number of functional relationships can not be expressed by analytical expressions, but only by images, tables and other forms.

In the process of a change, the quantity that changes is called a variable (in mathematics, it is often X, and Y changes with the change of X value), and some numerical values do not change with the variable, so we call them constants.

Independent variable (function): a variable related to other quantities, and any value in this quantity can find a corresponding fixed value in other quantities.

Dependent variable (function): it changes with the change of independent variable. When the independent variable takes a unique value, the dependent variable (function) has and only has a unique value corresponding to it.

Function value: in a function where y is x, x determines a value, and y determines a value accordingly. When x takes a, y is determined as b, and b is called the function value of a.

Let a and b be non-empty number sets. If any number x in set A has a unique number corresponding to it according to a certain correspondence F, it is called the mapping from set A to set B as a function, and it is recorded as or.

Where x is called the independent variable, the function of x, the set is called the domain of function, the y corresponding to x is called the function value, and the set of function values is called the range of function, which is called the corresponding rule. Among them, the definition domain, the value domain and the corresponding rules are called the three elements of a function.

Definition domain, value domain and corresponding rules are called the three elements of a function. Generally written. If the domain is omitted, it generally refers to a set of meaningful functions.

References:

Baidu Encyclopedia-Function