So we guess that the relationship between equation and function is also a one-to-one relationship. An equation corresponds to a unique linear function, and the solution of a linear equation corresponds to the value of the independent variable under this specific function value, which is reflected in the image as the abscissa under a specific ordinate. It just makes people feel amazing, and math is amazing. Miracles go far beyond this. Let's look down: Can you imagine what would happen if I replaced this equal sign with an unequal one?
Through today's study, in fact, we found another solution to the linear equation, that is, chasing points on the corresponding linear function image. We have learned to solve inequalities before. What are the similarities and differences between solving equations and solving inequalities? The most noteworthy place is the sign change of inequality symbols, such as-2x+1> 3. When the left and right sides are divided by a complex number at the same time, the sign of inequality should change direction. So what is the relationship between the inequality reflected in the image and the function?
Think about the second question on page 96: 3x+2 >; 2; 3x+2 >0; 3x+2 >- 1。 What are the similarities and differences between these three inequalities? Explain these three inequalities from the perspective of function?
It can be seen that these three inequalities are the same on the left and different on the right. From the function point of view, it is equivalent to finding the range of independent variables when the function y=3x+2 is greater than 2,0 and-1 respectively. Reflected in the image, intuitively speaking, when the range of the ordinate is greater than 2,0 and-1 on the straight line of y=3x+2, how to find the corresponding range of the abscissa? Let's look at the picture on page 97 of the textbook. Through today's study, I believe you must have a deeper understanding of linear equation, linear inequality and linear function. In short, there is a one-to-one correspondence between them. Let's practice a few questions. Exercise Book 106 Page 3, 4 questions; Page 107 1, 2 questions.
Today, I successfully put some students to sleep again. My goal is that one day no one will sleep, not forced but attracted.
The first experiment found that the word-for-word manuscript was indeed too few words. The above content was about ten minutes, and the rest was improvisation, which was unexpected. But I really think it's better to write it out than to just have a look, get to know it and go directly to the stage to talk about the students' reactions. Moreover, if I can speak with some relevant practical knowledge instead of textbooks, I think it will attract students' attention more.
Think about it, too. I remember when I was in college, there was a teacher named Gao Shu. When I give a lecture, I can constantly insert some jokes or stories. In order to listen to this, I forced myself to listen carefully. Otherwise I'm afraid I'll miss something interesting. He just thinks that college Chinese can speak advanced mathematics. It's really powerful. Now I can understand why teachers in New Oriental have to write prepared paragraphs into word-for-word drafts in advance when preparing lessons. All the wonderful moments are long-term ability training. I don't know how he prepares lessons in private. Every time I see him on campus, I always want to talk to him, and I respect him very much.
Another thing that needs to be understood in advance is that it is impossible to give a lecture verbatim in class, and it is impossible to engrave every word into your mind. The function of the word-for-word draft is to clarify one's own ideas, and to polish and revise this idea repeatedly, that is, to write one's own content, so it will be more handy to stand on the podium and speak. Actually, you can prepare a reminder card with an outline. It would be better this way.
Supplement: The demonstration process of the image is as follows: We regard the left side of the inequality as an analytical expression of a linear function and the right side as a function value. The process of solving inequality can be read from the image. It is to observe the image of the function. When the function value is within a certain range, look at the value range of the corresponding independent variable, which is the solution set of inequality. The content of this chapter is a good way to show abstract functions intuitively with images and combine numbers with types. The process of knowing the world is like this. Show the abstract world you see in concrete language to distinguish authenticity. The more you understand the operating mechanism of this world, the higher the efficiency of understanding this world will be. The process of education is the process of learning this ability. I have always felt that the best education is to educate yourself, that is, to take the initiative to explore, analyze and demonstrate.
This ability to analyze and demonstrate can't be taught directly in school, but it is unconsciously exercised by studying this knowledge carefully and practicing a certain skill repeatedly. If we can consciously record and reflect, the effect will of course be better. When you scratch your head for every math problem and keep looking through the textbook materials in order to solve a problem, your ability of analysis and thinking will be well exercised, that is to say, if you don't get good grades, you won't get anything. As long as you persist in doing these tasks, even if your grades are not good, you will benefit for life in the future. On the other hand, if you can do these jobs over and over again, you can't fail to get good grades. It's a matter of time. Therefore, no matter what the situation is now, no matter what others say, no matter whether others believe you or not, I hope you will continue to do it, and I encourage you to do it. I hope that one day you can really do it and show off your achievements and your gains to me.