1, variables and constants

In a certain change process, the quantity that can take different values is called a variable, and the quantity whose value remains unchanged is called a constant.

Generally speaking, there are two variables, X and Y, in a certain change process. If for each value of X, Y has a unique and definite value corresponding to it, then X is an independent variable and Y is a function of X. ..

2. Resolution function

The mathematical formula used to express functional relationship is called resolution function or functional relationship.

The whole set of values of independent variables that make a function meaningful is called the range of independent variables.

3. Three representations of functions and their advantages and disadvantages.

(1) analytical method The functional relationship between two variables can sometimes be expressed by equations containing these two variables and symbols of digital operations. This representation is called analytical method.

(2) List method lists a series of values of independent variable X and the corresponding values of function Y into a table to represent the functional relationship. This representation is called list method.

(3) Image method The method of using images to express functional relationships is called image method.

4. General steps of drawing images with resolution function.

(1) List: List gives some corresponding values of independent variables and functions.

(2) Point tracking: Take each pair of corresponding values in the table as coordinates, and track the corresponding points on the coordinate plane.

(3) Connection: according to the order of independent variables from small to large, connect the tracked points with smooth curves.

Learning function

(0) Constant function (1) Direct proportional function, Inverse proportional function (2) Linear function (3) Quadratic function

? Extended data

Determination of Positive Proportional Function and First Resolution Function

Determining the proportional function is to determine the constant k(k0) in the definition of the proportional function. To determine a linear function, we need to determine the constants K and b(k0) in the definition of linear function. The general method to solve this kind of problem is the undetermined coefficient method.

The image of (1) linear function is a straight line passing through two points. The larger the value of |k|, the closer the image is to the y axis.

(2) when k >; 0, the image passes through one or three quadrants, and y increases with the increase of x; From left to right, the image is rising (lower left and higher right);

(3) When k < 0, the image passes through two or four quadrants, and y decreases with the increase of x, and from left to right, the image decreases (the left is higher and the right is lower);

(4) When b>0, the intersection point (0, b) with the Y axis is on the positive semi-axis; When b<0, the intersection (0, b) with the Y axis is on the negative semi-axis. When b = 0, the linear function is a proportional function and the image is a straight line passing through the origin.

(5) When several straight lines are parallel to each other, the values of k are equal and b are not equal.

Extended Data Baidu Encyclopedia-Function