The relationship between primary function knowledge points and vectors and linear geometry

1. Knowledge overview.

The primary function is one of the main members of the function family, is the basis for studying two variables and learning other functions, its expression is simple, the nature is not complicated, but the application in our daily life is very extensive, and the connection with other functions is also very close, many practical problems as long as we pay attention to careful observation, careful analysis, timely transformation of the problem into a function model, and then use the properties of the function can be solved

2. Knowledge points.

If the relationship between two variables x and y can be expressed as y kx+b(k≠0), then y is said to be a primary function of x In particular, when b 0, y is said to be a proportional function of x, that is, the proportional function is a special case of the primary function, and the primary function contains a proportional function, which is proportional and must be a one-time function, but the one-time function is not necessarily a proportional function For example, y x is a proportional function and a one-time function, and y 2x 3 is a one-time function, but it is not a proportional function

Function properties: The change value is proportional to the change value of the corresponding x, and the ratio is kNamely:

y=kx+b(k,b is constant, k≠0), when x increases m, k(x+m)+b=y+km, km m=k 2.When x=0, b is the point of the function on the y-axis, and the coordinates are (0,b).

3 When b = 0 (i.e. y=kx), the image of the primary function becomes a proportional function, which is a special one-time function. 4.In two primary function expressions:

When k in the expression of the two primary functions is the same and b is also the same, the images of the two primary functions coincide. When k in the expression of the two primary functions is the same and b is not the same, the images of the two primary functions are parallel. When k in the expression of the two primary functions is not the same and b is not the same, the images of the two primary functions intersect; When k in the expression of the two primary functions is not the same and b is the same, the images of the two primary functions intersect at the same point (0,b) on the y-axisIf the relationship between two variables x and y can be expressed as y=kx+b (k,b is a constant, k is not equal to 0), then y is said to be a primary function of x.

Image nature. 1 Practices and Graphics: Through the following 3 steps:

1) Lists. (2) tracing points; [Generally take two points, according to the principle of "two points to determine a straight line and town", it can also be called "two-point method".]The general image of y=kx+b(k≠0) can be drawn with straight lines through (0,b) and (-b k,0).

The image of the proportional function y=kx(k≠0) is a straight line passing through the coordinate origin, generally taking two points: (0,0) and (1,k). (3) Connecting lines, you can make an image of a function - a straight line. Therefore, to make a function of the image, you only need to know 2 points and connect them into a straight line.

In general, the intersection points of the function image with the x-axis and y-axis are -k/b and 0, 0 and b), respectively2 Properties: (1) Any point p(x,y) on a primary function satisfies the equation:

y=kx+b(k≠0).(2) The coordinates of the intersection point of the primary function and the y-axis are always (0, b), and the image of the number of the intersection of the x-axis is always proportional to (-b k, 0). 3 A function is not a number, it refers to the relationship between two variables in a certain process of change.

4 k,b and the quadrant of the function image: y=kx (i.e., b is equal to 0, y is proportional to x): when k>0, the straight line must pass through.

1. In the third quadrant, y increases with the increase of x; When k0,b>0, then the image of this function passes through the first.

one, two, and three quadrants; When k>0,b