If you want to learn functions well, you must first master the basic definitions and corresponding image features, such as definition domain, value domain, parity, monotonicity, periodicity, symmetry axis and so on. Many students have entered the misunderstanding of learning function, thinking that as long as they master the problem-solving methods, they can learn mathematics well. In fact, they should master the most basic definitions before they can learn how to solve problems well. In the final analysis, all problem-solving methods should start from the basic definitions, and it is best to master the algebraic expressions and image characteristics of these definitions and properties.
Second, keep in mind several basic elementary functions and their related properties, images and transformations.
There are several basic elementary functions in middle school: linear function (linear equation), quadratic function, inverse proportional function, exponential function, logarithmic function, sine and cosine function and tangent cotangent function. All function problems are based on these functions, but in different forms, and finally they can be solved through basic knowledge. There are also three kinds of functions, which are not found in textbooks. They often appear in college entrance examination and self-enrollment examination: y=ax+b/x, a function with absolute value and a cubic function. The properties of these functions, such as domain, range, monotonicity, parity, etc., and the characteristics of images should be studied well.
Third, image is the soul of function! If we want to learn function problems well, we should pay full attention to the problem of function image.
Looking through the function questions of college entrance examination over the years, we can find that there is a calculation, and almost 80% of the function questions are related to images. This requires children's shoes to pay more attention to the image of the function when learning the function, and to be able to draw, see and use pictures! Translation, scaling, flipping, rotation, composition and superposition of multi-attention function images.
Fourth, do more questions, ask more teachers and summarize more.
Doing more questions does not mean asking questions about sea tactics, but doing appropriate questions according to your own situation; The focus should be on summing up. What should we sum up? Summarize problems, methods, wrong questions, ideas, knowledge, etc!