Further understanding of the concept of function The definition of function has been described in junior high school. After entering high school, I learned mapping on the basis of learning set, and then I learned the concept of function, mainly to clarify the function from the perspective of mapping. At this time, I can use the functions that students already know, especially quadratic functions, as an example to better understand the concept of functions. Quadratic function is the mapping from set A (domain) to set B (range). : A→B, so that the element y=ax2+bx+c(a≠0) in the set b corresponds to the element x in the set a, and is denoted as f(x)= ax2+ bx+c(a≠0), where ax2+bx+c represents the corresponding rule and image of the element x in the domain. Students can further deal with the following problems: Type 1: When f(x)= 2x2+x+2 is known, find f(x+ 1). Here, f(x+ 1) cannot be understood as the function value when x=x+ 1, but only as the independent variable. Type ⅱ: let f(x+ 1) = x2-4x+ 1, and the problem of finding f(x) is understood as: under the known corresponding rule f, the image of the element x+ 1 in the domain is x2-4x+ 1, and the element x in the domain is found. Generally, there are two methods: (1) expressing a given expression as a polynomial of x+ 1. F (x+ 1) = x2-4x+1= (x+1) 2-6 (x+1)+6, and then use x+1to get f (x) = x2. Let t=x+ 1, then x = t-1∴ (t) = (t-1) 2-4 (t-1)+1= T2-6t+6. Type ⅲ: Draw the images of the following functions, and study their monotonicity through the images. (1) y = x2+2 | x-1|-1(2) y = | x2-1| (3) = x2+2 | x |-1Here students should pay attention to the relationship between these functions and. Master the function marked with absolute value as piecewise function, and then draw its image. Type Ⅳ let f (x) = x2-2x- 1, and the minimum value in the interval [t, t+ 1] is g(t). Find: g(t) and draw the image solution of y = g (t): f (x) = x2-2x-1= (x-1) 2-2. When x= 1, the minimum value of -2 is 1 ∈. 0)g(t)= -2, (0≤t≤ 1)t2-2t- 1, (t> 1) First, let the students understand the meaning of the question. Generally, a quadratic function has only a minimum value or a maximum value on the real number set r, but when the definition domain changes, the situation of taking the maximum value or the minimum value will also change. In order to consolidate and be familiar with this knowledge, students can be supplemented with some exercises. For example: y = 3x2-5x+6 (-3 ≤ x ≤- 1), find the range of this function. Third, the knowledge of quadratic function can accurately reflect students' mathematical thinking: Category V: Set quadratic function? (x)= ax2+bx+c(a & gt； 0) equation? Two roots of (x)-x = 0 x 1, and x2 satisfies 0.
Quadratic function has rich connotation and extension. As the most basic power function, we can take it as a representative to study the nature of functions, establish the relationship among functions, equations and inequalities, draw up endless and flexible mathematical problems, examine students' basic mathematical knowledge and comprehensive mathematical quality, especially distinguish students' ability to use mathematical knowledge and thinking methods to solve mathematical problems from the depth of solutions. The content of quadratic function covers a wide range, and this paper only discusses this point. I hope all my colleagues will pay more attention to this knowledge in senior high school mathematics teaching, so that we can learn more deeply. F (x 1) >: the internal realization of f (0), so when x∈(0, x1), f (x)