Linear function is the basis of learning function. Learn more functions in the future, especially the part of quadratic function. If you can't learn the first function well, you can hardly learn the second function. Therefore, we should work harder and spend more time on the study of elementary functions, so that we can learn knowledge less laboriously in the future. In fact, in my opinion, the knowledge of a function is the key, but these key points are not difficult and not difficult to understand, but remember, you still have to work hard. Here's some related knowledge for you, which should be in your file.

Basic concept of function: Generally speaking, there are two variables X and Y in a certain change process. If a value of X is given and the unique value of Y corresponding to X is determined accordingly, then we call Y a function of X, where X is an independent variable and Y is a dependent variable, that is, Y is a function of X. ..

When x=a, the function value is called the function value when x = a.

Defining and defining expressions

The independent variable x and the dependent variable y have the following relationship: y=kx (k is any non-zero real number) or y=kx+b (k is any non-zero real number and b is any real number).

It is said that y is a linear function of x at this time.

In particular, when b=0, y is a property of linear function of x.

The change value of 1.y is in direct proportion to the corresponding change value of x, and the ratio is k, that is, y=kx+b(k≠0) (k is any non-zero real number b, take any real number).

2. When x=0, b is the intercept of the function on the y axis.

3.k is the slope of the linear function y=kx+b, and k=tg angle 1 (angle 1 is the positive included angle between the linear function image and the x axis). Take it. Elephant. Pay. The negative proportional function is also a linear function.

2.

Nature:

Any point P(x, y) on the (1) linear function satisfies the equation: y=kx+b(k≠0).

(2) The coordinate of the intersection of the linear function and the Y axis is always (0, b), and the image of the proportional function always intersects the origin of the X axis at (-b/k, 0).

3. Function is not a number, it refers to the relationship between two variables in the process of a variable.

4. Quadrant where K, B and function images are located:

When y=kx (that is, b is equal to 0 and y is proportional to x)

When k > 0, the straight line must pass through the first and third quadrants, and y increases with the increase of x;

When k < 0, the straight line must pass through the second and fourth quadrants, and y decreases with the increase of x.

When y=kx+b:

When k>0, b>0, then the image of this function passes through the first, second and third quadrants.

When k>0, b<0, then the image of this function passes through one, three and four quadrants.

When k < 0, b<0, then the image of this function passes through two, three and four quadrants.

When k < 0, b>0, then the image of this function passes through the first, second and fourth quadrants.

When b > 0, the straight line must pass through the first and second quadrants;

When b < 0, the straight line must pass through three or four quadrants.

Particularly, when b=0, the image of the proportional function is represented by a straight line of the origin o (0 0,0).

At this time, when k > 0, the straight line only passes through one or three quadrants; When k < 0, the known point A(x 1, Y 1) of the function expression is determined once by a straight line passing through only two or four quadrants; B(x2, y2), please determine the expressions of linear functions passing through points A and B. ..

(1) Let the expression (also called analytic expression) of a linear function be y = kx+b.

(2) because any point P(x, y) on the linear function satisfies the equation y = kx+b.

So we can list two equations: y1= kx1+b ...

And y2 = kx2+b...②.

(3) Solve this binary linear equation and get the values of K and B. ..

(4) Finally, the expression of the linear function is obtained.