Many students remember formulas, some fixed functional properties or images, but they don't use them comprehensively. It's like giving an ordinary person a toolbox, but he can't assemble mechanical equipment as skillfully as a mechanic. Why? The reason is the same, I don't understand, I don't practice, the practice method is incorrect, and I don't have the relevant skills and methods.
The combination of functional knowledge will produce many changes, but these changes are usually inevitable. Only by in-depth and continuous analysis and research can we grasp its laws.
Many students find functions difficult to learn because they can't adapt to the changes of functions and are not good at grasping the invariance in changes.
We can understand this function from several aspects:
A function has three elements: corresponding rules, definition fields and value fields.
Many functions include images, monotonicity, symmetry (including parity), periodicity, some extreme values and maxima, images of some similar functions passing through special fixed points and so on.
Learning function concretizes abstract problems and simplifies complex problems.
For example, some functions are very complex, and their images are also very complex. By studying the properties and images of common functions related to them, we should adopt indirect methods to transform, analyze and judge them.
When we study functions, we should be good at simplification and simplification, because functions are changeable. If we learn simplification, we can master more complex knowledge by using existing knowledge.
The method of function summation. The commonly used methods of functions are: method of substitution, assignment, simplification, combination of numbers and shapes, equivalent substitution, separation of variables, separation of constants, construction and so on.