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一、利用解方程判断函数零点个数例1函数f(x)={x2+2x-3,x≤0,-2+ln x,x>0的零点个数为A.0 B.1 C.2 D.3解当x≤0时,令x2+2x-3=0,解得x=-3;当x>0时,令-2+ln x=0,解得x=e2.所以,函数f(x)有2个零点.选C.二、利用函数图像判断函数零点个数1.直接观察函数图像与x轴的交点个数根据函数零点的定义,可作出函数y=f(x)的图像,它与x轴的交点个数就是函数零点个数.此方法适合容易作出图像的函数.如例1可直接作出函数图像,如图1所示.由图1可知,此函数有2个零点.2.一分为二转化为两个函数图像的交点个数
First, the use of equations to determine the number of zero function Example 1 The function f (x) = {x2 + 2x-3, x ≤ 0, -2 + ln x, x> 0 zero the number of A.0 B.1 C .2 D.3 Solution Let x2 + 2x-3 = 0 when x≤0 and solve for x = -3. When x> 0, let -2 + ln x = 0 and solve for x = e2. So , The function f (x) has two zeroes C. Select the second, use the function image to determine the number of zero points 1. Direct observation function image and the x-axis number of intersections According to the definition of the function zero, the function y = f x) of the image, the number of its intersection with the x axis is the number of zero function. This method is suitable for easy to make a function of the image as in Example 1 can be directly function image, as shown in Figure 1. Figure 1 shows that this function There are two zero points .2. The number of intersections converted into two function images in one divided into two