1. Understand the concepts of proportional function, linear function and inverse proportional function;

2. Understand the properties of proportional function, linear function and inverse proportional function;

3. Will draw their images;

4. Analytic expressions of proportional function, inverse proportional function and linear function will be obtained by using undetermined coefficient method.

content analysis

1, linear function

(1) linear function and its image

If y=kx+b(K, b is constant, K≠0), then y is called a linear function of x.

In particular, if y=kx(k is a constant, K≠0), then y is called the proportional function of x.

The image of the function is a straight line. To draw an image of a function, just draw two points first and then connect them into a straight line.

(2) Properties of linear functions

When k>0, y increases with the increase of x, and when k

2. Inverse proportional function

(1) inverse proportional function and its image

So, if y is an inverse proportional function of x.

The image of the inverse proportional function is a hyperbola with two branches. The image of inverse proportional function can be drawn by tracing points.

(2) Properties of inverse proportional function

When K>0, the two branches of the image are in the first, second and third quadrants respectively, and in each quadrant, Y decreases with the increase of X;

When k < 0, the two branches of the image are in the second and fourth quadrants respectively, and in each quadrant, y increases with the increase of x.

3. The undetermined coefficient method

First, the unknown number in the formula is set, and then the unknown coefficient is obtained according to the conditions, so the writing of this formula is called undetermined coefficient method. Analytic expressions of linear function, quadratic function and inverse proportional function can be obtained by undetermined coefficient method.

Key points and frequently asked questions in the exam

1

Investigate the definitions and properties of proportional function, inverse proportional function and linear function. Related questions often appear in multiple-choice questions.

2. Comprehensively investigate the images of direct proportion, inverse proportion and linear function. The characteristic of the exercise is to examine the images of two functions in the same rectangular coordinate system, and the question type is multiple choice.

3. The analytic expressions of direct proportion, inverse proportion and linear function are examined by undetermined coefficient method. The frequency of related exercises is very high, and the types of exercises include intermediate solution problems and selective synthesis problems.

4. Using functions to solve practical problems and get the maximum value is a new feature of the application problems in the senior high school entrance examination in recent three years.

Requirements and proposition trend of senior high school entrance examination

Function is an important embodiment of the combination of numbers and shapes, and it is a compulsory content in the senior high school entrance examination every year. The concept of function mainly examines the range of independent variables, the changing images of independent variables and dependent variables, and the plane rectangular coordinate system in the form of filling in the blanks, which generally accounts for about 2%. The univariate function is closely related to the univariate equation, which is the compulsory content of the senior high school entrance examination. Generally, it is examined in the form of filling in the blanks, multiple-choice questions, solving problems and comprehensive questions, accounting for about 5%. The image and properties of inverse proportional function are often examined in the form of objective questions. Pay attention to the connection between inverse proportional function and practical problems and highlight its application value. Score 3-6; Quadratic function is a very important content in junior high school mathematics, and it is a hot spot in the senior high school entrance examination, and it often appears in the test paper as the finale. Requirements: be able to determine the expression of quadratic function and understand the meaning of quadratic function by analyzing the actual problem scenario; The image of quadratic function can be drawn by tracing points, and the properties of quadratic function can be analyzed on the image; According to the formula, the vertex, opening direction and symmetry axis of the image can be determined, and practical problems can be solved. Will find an approximation of a quadratic equation.

20 10 still mainly investigates the range of independent variables and the change image between independent variables and dependent variables. Images and properties of linear functions; Investigate the understanding of the concept and nature of inverse proportional function in practical problems. We will continue to examine the quadratic function, focusing on its comprehensive application with algebra and geometry knowledge, and strengthen the practical application of quadratic function.

Examination-oriented countermeasures

1, understand the concept of function and the coordinate characteristics of some points in the plane rectangular coordinate system.

2. Train the image recognition of changes between independent variables and dependent variables, and truly understand the relationship between images and variables.

3. Master the general form and image of a linear function.

4, master the increase or decrease of a function, distribute quadrants, and draw.

5. Clarify the characteristic image of inverse proportional function, and improve the practical application ability.

6, firmly grasp the concept and nature of quadratic function, pay attention to understand the significance of quadratic function in the actual situation, pay attention to the comprehensive problems related to quadratic function, and clarify the relationship between knowledge.