Matching method refers to the method of making functions by formula. It is known that some functions find the analytic expression of another function, and this method is often used.
Example 1. F(x+3) is known.
Analysis: This is an abstract equation with unknown function f(x). From the definition of function f(x), we can see that when the definition domain and corresponding law f of the function remain unchanged, the algebraic expression of letters or even other letters is changed by independent variables, which has no influence on the function itself. This kind of problem is solved by using this property.
Second, the substitution method
Substitution refers to the mathematical method of substituting one quantity for another. Let's take the above topic as an example.
set up
rule
Third, the undetermined coefficient method
The undetermined coefficient method refers to the method of setting the resolution function of the undetermined coefficient first and then trying to determine the undetermined coefficient according to the conditions provided by the topic.
Example 2. It is known that the function f(x) is a linear function passing through points (1, 2), (2, 5). Find the analytic formula of function y=f(x).
Analysis: Given the types of functions in this question, we only need to establish the corresponding analytical model and solve the coefficients through equations.
Fourth, the elimination method
Elimination method refers to the method of finding the resolution function by eliminating some elements.
Example 3. Let f(x) satisfy the relational expression and find the analytical expression of the function.
Analysis: If the given topic is regarded as two elements, then the equation can be regarded as a binary equation, and x can be exchanged with 1/x to form a new equation.
Verb (abbreviation of verb) formula method
Refers to the method of finding the resolution function by using the known formula.
For example, Galileo experimented with the leaning tower of Pisa, and two iron balls fell freely, so as to find the relationship between the displacement of the balls and time.
Analysis: Because the free-falling body is in uniform linear motion, the relationship between the displacement S of uniform linear motion and time T is S = vo t+a t2, vo is the initial velocity, and A is the acceleration. Therefore, we can substitute the initial velocity and acceleration of free fall into the above formula and get the functional relationship between time and displacement of free fall.
Solution: Because the acceleration of free fall is G and the initial velocity is 0.
According to the formula of uniform linear motion, the functional relationship between displacement h of free falling body and time t is as follows:
H= g t2
Of course, we can also use the method of control variable analysis and other methods to find the analytical expression of the function.
Personally, I think learning function should pay attention to the following points:
1。 Defining the domain and value domain is the premise of solving the function correctly.
2。 General topics will give some basic knowledge, so we should clearly understand the basic concepts:
For example:
Odd (even) functions and their equivalent mathematical expressions (for example, odd function is equivalent to f(x)=-f(-x)).
Quadratic function, power function, exponential function, logarithmic function, images and properties of these functions.
Proof of monotonic increase (decrease) of function in interval.
Proof of periodic function.
3。 Cultivate the thinking of combining numbers and shapes, flexibly convert mathematical symbol language and graphic language, remember the images and properties of basic functions, and do exercises against textbooks at first.
To understand the above concepts, no matter how the topic changes, it is a familiar pattern, which can be practiced through certain practice at most. Therefore, the learning function focuses on the basic definition and its equivalent mathematical expression, and the combination of numbers and shapes is three key factors.