fq5555:2013高一数学必修1课件教师用书第四章章末小结知识整合与阶段检测(北师大版)_图文

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第 章末 四 小结 章

知识

函 整合

数 与阶

应 段检





核心要点归纳 阶段质量检测

一、零点与方程的根 1.函数y=f(x)的零点就是方程f(x)=0的根,也是函数 y=f(x)的图像与x轴交点的横坐标,因此求函数y=f(x)的零点, 其实就是解方程f(x)=0,求其根,方程有几个根,函数就有 几个零点. 2.判断y=f(x)零点的个数有三种方法:①解方程f(x)=0, 求根的个数;②画函数y=f(x)的图像,看图像与x轴交点的个 数;③将g=f(x)转化为g(x)=φ(x),观察函数y=g(x)和y=φ(x) 的交点的个数.

3.利用零点存在性定理判断零点时,要注意两个条件: (1)函数在区间[a,b]上的图像不间断,(2)f(a)·f(b)<0, 缺一不可.但该定理只能判断出函数在区间上存在零点,而 不能确定零点的个数. 4.函数在区间[a,b]上的图像不间断,且函数在区间 (a,b)上单调,若f(a)·f(b)<0,则函数在区间(a,b)上有且只 有一个零点.

二、二分法 1.对于函数y=f(x)的图像在区间[a,b]上不间断,且 f(a)·f(b)<0的函数y=f(x),通过不断地把函数f(x)的零点所在 的区间一分为二,使区间的两个端点逐步逼近零点,进而得 到零点近似值的方法叫二分法. 2.运用二分法的前提条件是先判断函数零点所在的区 间,且二分法仅对函数的变号零点适用. 3.求函数零点近似值时,所要求的精确度不同,得到 的结果也不相同.精确度要求越高,零点近似值所在的区间 长度越小,计算过程越长.

三、函数建模 1.解答函数应用题的一般步骤是:
2.函数模型的应用,一方面是利用已知函数模型解决 问题;另一方面是建立恰当的函数模型,并利用所得函数 模型解释有关现象,对某些发展趋势进行预测.

点击下列图片进 入阶段质量检测


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