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Before we learned about quadratic function . Everyone has a basic impression of function . Starting today, we will start learning the system's function related knowledge!
What is a function
About functions, students should be familiar with functions, because in junior high school, we have already come into contact with functions, so can you tell us what is a function?
Many students will say that functions can represent the relationship between two variables, which is indeed the case, but this is not rigorous enough.
rigorously speaking, a function is a correspondence. Through this correspondence, each element in number set A can find the unique and determined elements in the number set B to correspond to it (the number set is a collection. Students who don’t know about the set and elements need to review it!).
From this, to more accurately, we can get the concept of function:
Three elements of function
According to the concept of function, we can find that three components are required to form a function, namely definition domain , correspondence and value domain.
students will find that during the process of doing the questions, most of the examination of functions will revolve around the three elements of the function, such as two elements are known to require another element, etc.
3 :
1) Simple domain definition method: When students seeking the domain definition, the first thing they need to consider is whether the functional formula is true. For example, the denominator of the fraction cannot be 0, the base number of the quadratic root formula cannot be less than 0, etc.;
2) Composite function definition method: For composite functions, the domain of the original function of is often given first. Students only need to use the transmutation method to find the domain of the composite function.
functions are equal:
When the domain and correspondence of two functions are exactly the same, these two functions are equal;
Regarding the correspondence, we will supplement the learning of "mapping" later, and interested students can conduct extended learning.
3 evaluation domain:
3 queries the value range of the function. When we understand the properties of the function, the value range corresponding to the given domain can also be obtained. Of course, when the domain is an individual number, students can also directly bring it into the value range;
In addition, students will find that the value range of the function is a subset of the set B, because the value range is the value corresponding to the given domain, but the value range is not necessarily the real subset of the set B !
(Students who forget what subsets and real subsets are, need to review!)
expression
When we describe the definition domain and value domain, we often use "range", Mathematically, we will use "interval" to represent this "range":
Then, the interval of real set R is expressed as (-∞, +∞), where ∞ is read as "infinity", and -∞ and +∞ can be used to represent the interval of "opening" on one side, for example, the interval of x1 is expressed as (-∞, 1).
Today, we learned the concept of functions, three elements and other knowledge points, hoping to help students better study high school mathematics!
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