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课题:函数初步适用年级:高三年级学期:2006～2007学年度第一学期要点提示函数思想贯穿高中数学始终,函数一章历来是高考的重点,试题大致分为两类:一是考查函数的基础知识和基本方法;二是对函数与其他数学问题如导数、方程、不等式和数列的综合考查．函数的三要素是对应法则、定义域和值域．函数y =f(x)中x与y的对应关系可采用解析法、列表法、图像法等形式,其中解析法应用最普遍,函数的解析表达式的确定常采用待定系数法．函数定义域的确定常采用解不等式(组)的方法;而函数值域确定的基本方法是由自变量x所满足的不等式,通过变换导出因变量y的不等式．函数的奇偶性是函数值所满足的一个特定的等量关系;函数的单调性则是不等式x1f(x2)的转换关系,或是与f’(x)>0或f’(x)<0成立与否密切相关．函数图像直观形象地反映了函数的性质,要深刻体会数形结合的数学思想,并应用数形结合的方法解决函数问题．
Topic: Functions Initially Applicable Grades: Senior Year 3 Term: 2006-2007 First Semester Key Points Tips The function ideology runs through high school mathematics, and the function chapter has historically been the focus of the college entrance examination. The questions are broadly divided into two categories: First, the examination function Basic knowledge and basic methods; the second is a comprehensive examination of functions and other mathematical problems such as derivatives, equations, inequalities and series. The three elements of the function are the correspondence law, the definition domain and the value domain. The corresponding relation between x and y in the function y = f(x) can be in the form of analytical method, list method, image method, etc. The analytical method is most commonly used, and the analytical expression of the function is often determined by the undetermined coefficient method. The definition of the function definition domain often uses the method of solving inequalities (groups); the basic method for determining the function value domain is the inequality satisfied by the independent variable x, and the inequality of the dependent variable y is derived by transformation. The parity of a function is a specific equivalent relationship that the function value satisfies; the monotonicity of the function is the conversion relationship of inequality x1f(x2). , or is closely related to whether f’(x)>0 or f’(x)<0 is established or not. The function image intuitively and vividly reflects the nature of the function. It is necessary to deeply understand the mathematics idea of the combination of number and shape, and apply the combination of number and shape to solve the function problem.