One. Proportional function
1,. Picture: Analytical formula: y=kx
(k≠0) A straight line passing through the origin. Is a special linear function.
2. Attribute: When k > 0, the image passes.
One or three quadrants. Y increases with the increase of x and decreases with the decrease of x.
When k < 0, the image passes.
In the second and fourth quadrants, y decreases with the increase of x, and y increases with the decrease of x.
3. Drawing method: Take any point and draw a straight line from the origin.
Second, the linear function
1, image: analytical formula: Y=kx+b(k≠0), which is the proportional function Y=kx.
(k≠0), translate up and down by b units.
There are two intersections with the coordinate axis. Found A(0, y), B(x, 0)
x，y
Draw a straight line after the values of these two points
All right.
2, and the nature of the proportional function is the same. The greater the absolute value of k, the closer the image is to the Y axis, and vice versa. K= 1, figure
For example, it is the bisector of one or three quadrants. When k=- 1, it looks like the bisector of two or four quadrants.
Test center: images of two linear functions are often used to illustrate the preferential conditions of two kinds of telephone charges. (There is a landline fee, a function; The images of the two functions have an intersection point, the abscissa represents the talk time, and the ordinate represents the charging situation.
The abscissa value of the intersection point indicates the call time, and the ordinate value indicates that the two charges are the same. The intersection is on the right. With the increase of call time, the image of the primary function is low, indicating that the landline fee is preferential. If the intersection is on the left, it means that the call time is below this range, and there is no discount for landline charges. By analogy, other similar topics are not explained one by one.
Third, the inverse proportional function
1, image: analytical formula: y=k/x(k≠0) The image is a hyperbola.
2. properties: when k > 0, the image is in one or three quadrants, y decreases with the increase of x, and y increases with the decrease of x. ..
When k < 0, the image is in two or four quadrants, y increases with the increase of x, and y decreases with the decrease of x.
The image will never intersect the coordinate axis. The two branch of that image are symmetrical about the origin.
Test center: Learn in a coordinate system by combining linear functions. Generally, it is to find the coordinates of intersection points. Analysis; When they intersect, the x and y of the two equations are equal, so let.
k 1x=k2/x
If they are equal, you can get the value of x, and there are two. If you substitute them into the original analytical formula, you can get y, so you can know the coordinates of the point.
The more complicated problem is that the linear function intersects with the inverse proportional function to form a triangle and calculate the area of the triangle. Or tell you the area, so you can be sure.
Analytic expression of function.
In a word, to find the analytical formula is to analyze what kind of function it is, so as to establish the corresponding analytical formula and substitute it for evaluation. We call it the undetermined coefficient method. Detailed problem-solving ideas and methods and skills need to be explained in combination with some topics. You send it, ask questions, and I can draw more pictures for you.