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Last week we learned the concept and three elements of the function . Do students still remember it? If you forget it, remember to review it in time! Common representation methods of
function
junior high school, we have learned about three common representation methods of functions, namely parsing method, list method and image method. Do you know the scope of application and advantages and disadvantages of these three methods?
parsing method:
uses mathematical expression to represent the correspondence between two variables, that is, functional expression method. Its advantage is that it is relatively concise and clear, and can obtain the value domain (function value) according to the characteristics of the function formula when the domain is known ( independent variable ), but this method is often very abstract, so in the subsequent learning process, the analytical method is often used in combination with the image method;
list method:
list method:
list method:
list method:
list method: html ml4
uses a table to represent the correspondence between two variables. The advantage of this method is that it does not require calculation to clearly see the function value, which is suitable for problems such as bank interest rate tables. However, you will also find that the capacity of the list method is very limited, discrete, and not coherent;
Image method:
uses an image to represent the correspondence between two variables. Compared with the first two, the image method is more intuitive and can see the trend of change. However, the process of extracting images is often complicated, so it is often used in combination with analytical methods.
segment function
segment function refers to a function that has different correspondences for different value ranges of independent variables within the definition domain .
What students need to pay attention to is:
1) Although the segmented function includes several different correspondences, it is still a function;
2) segmented function The domain of a number is the "union" of several parts (what is a combination, do you remember it?);
3) Different parts of the domain of the segment function cannot intersect;
4) Since the segment function includes several correspondences, the image of the segment function is not necessarily a continuous curve.
Extended Learning - Mapping
People's Education Press textbook deleted the mapping content, but in order for students to better understand the functions, we briefly understand the basic concepts of mapping, and this part does not require rigid requirements! The definition of
mapping is:
where "f:A→B" represents the mapping of A to B, and "f:B→A" represents the mapping of B to A. These two are not the same mapping!
mapping also has three elements, namely two sets and one corresponding rule . This is very similar to a function. However, a function requires that two sets must be sets of numbers, and the mapping does not have special requirements for the set.
Therefore, we can say that functions are a special mapping.
Today, we learned the knowledge points such as function representation methods, segmented functions, etc., hoping to help students better study high school mathematics!
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