Mathematics has been applied in many different fields, including science, engineering, medicine and economics. The following is a summary of the knowledge points of the elementary function of mathematics, which I compiled. Welcome to refer to!

I. Definitions and definitions:

Independent variable x and dependent variable y have the following relationship:

y=kx+b

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

In particular, when b=0, y is a proportional function of x, that is, y=kx(k is a constant, k? 0)

Second, the properties of linear function:

The change value of 1.y is in direct proportion to the change value corresponding to x, and the ratio is k, that is, y=kx+b(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.

Iii. Images and properties of linear functions:

1. Practice and graphics: Through the following three steps.

(1) list;

(2) tracking points;

(3) Connecting lines can make straight lines into images of linear functions. So the image of a function only needs to know two points and connect them into a straight line. (Usually find the intersection of the function image with the X and Y axes)

2. Property: (1) Any point P(x, y) on the linear function satisfies the equation: y = kx+b (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. Quadrant where K, B and function images are located:

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

When b=0, the straight line passes through the origin.

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

Especially, when b=O, the straight line passing through the origin o (0 0,0) represents the image of the proportional function. At this time, when k>0, the straight line only passes through the first and third quadrants; When k < 0, the straight line only passes through the second and fourth quadrants.

Fourth, determine the expression of a linear function:

Known point A(x 1, y1); 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) Since any point P(x, y) on the linear function satisfies the equation y = kx+b, two equations can be listed: y 1 = kx 1+B 1 and y2 = kx2+B2.

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

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

Five, the application of linear function in life:

1. When the time t is constant, the distance s is a linear function of the velocity v .. s=vt.

2. When the pumping speed f of the pool is constant, the water quantity g in the pool is a linear function of the pumping time t, and the original water quantity s in the pool is set. G = S- feet.

Six, commonly used formula:

1. Find the k value of the function image: (y 1-y2)/(x 1-x2).

2. Find the midpoint of the line segment parallel to the X axis: |x 1-x2|/2.

3. Find the midpoint of the line segment parallel to the Y axis: |y 1-y2|/2.

4. Find the length of any line segment:? (x 1-x2) 2+(y 1-y2) 2 (note: the sum of squares of (x 1-x2) and (y 1-y2) under the radical sign).

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