In the whole junior high school mathematics, function occupies a very important position in algebra, which is the key and difficult point of senior high school mathematics. In the whole junior middle school mathematics, we need to learn four kinds of functions: proportional function, first-order function, inverse proportional function and quadratic function, among which proportional function is the most basic and special linear function.
Although the proportional function is simple, it is the basis of the whole junior middle school function learning. The image of a linear function is obtained by translating the image of a direct proportional function up and down, and the direct proportional function and the inverse proportional function are often combined in the examination. Therefore, if you want to learn junior high school functions well, you must start with the proportional function.
The study of proportional function mainly includes four parts: the concept of proportional function, image and property, function relationship and application, in which the concept of proportional function is the foundation, and the image, property and relationship are the key points.
Many students don't know the clue and how to start when learning functions. They share their knowledge about the proportional function, organize the knowledge points and necessary exercises of the proportional function, and master most of the contents of the proportional function by mastering these basic knowledge points and questions.
The role of mathematics:
Mathematics has a wide range of applications.
Mathematics is quite important. This can be seen from the breadth and length of subject setting. A person will learn mathematics from primary school (even kindergarten) until high school, university and even graduate students. Let's take a look at the subject setting in universities. It is not difficult to find that many subjects will take mathematics as an important research method.
These include: all natural science disciplines-that is why people call mathematics the language of science; Mathematics will also be used in social science disciplines-because statistics will be used as long as data processing is involved, and probability knowledge will inevitably be used; Engineering technology-Engineering technology is the application of mathematical theory. Economics-the subject dealing with numbers will of course use mathematics.
Learning mathematics can train people's thinking.
Mathematics is not magic. Mathematics may be abstract, but this abstraction is extracted from the concrete. This was even more obvious in the seventeenth century when numbers and shapes were unified. Mathematics originated from people's need to solve practical problems, and problem-solving thinking also runs through the whole process of mathematics development.
Therefore, learning mathematics can train people's problem-solving ability, which is embodied in analytical thinking in the way of thinking. Analytical thinking is to transform and split complex and detailed information into many small and basic parts for analysis. Analytical thinking is a relatively linear and gradual operation. It can be decomposed into the following steps:
Collect relevant information, facts and evidence to find out the key to the problem;
Use logic and reasoning to process information and simplify complex problems;
Discover patterns and trends;
Find out the causal relationship, understand the correlation and relationship, and draw appropriate conclusions.
The role of mathematics in the development of science and technology.
Mathematics is an ancient subject. Scientific research shows that human beings are not the only creatures that can recognize numbers. Some animals also show a basic understanding of quantity, and they can distinguish one, two and many differences. This shows that the concept of human use of numbers has a long history.
It is conceivable that many situations in prehistoric human life will use mathematical knowledge, such as the length and distance of seasons, food distribution and so on. None of these will use mathematics.
In human history, the importance of mathematics to human development can be fully demonstrated. These ancient countries in history have demonstrated a high level of mathematics application. In fact, as far as modern mathematics is concerned, the knowledge at that time could not be called "mathematics", but just some experience; The difference between experience and real mathematics is that experience has not been proved.