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在高中函数学习过程中,我们经常要解决一类含绝对值函数的最值问题,如:求函数f(x)=x-3+x+5的最小值.探究这一类问题后发现,一般常用处理方法有两种:一是将其转化为分段函数,通过计算或观察其图像得出函数最值及相应x的取值,这种方法的出发点是数——函数,主要使用了代数手段,是通性通法;二是利用绝对值的几何意义,通过观察数轴得到函数最值及相应x的取值,这种方法的出发点是形——数
In the process of high school function learning, we often solve the most value problem of a class of absolute value function, for example: Find the minimum value of function f (x) = x-3 + x + 5. Explore this kind of problem, Commonly used in two ways: First, it will be transformed into a piecewise function, by calculating or observing the image obtained the value of the function and the corresponding value of x, the starting point of this method is the number - function, the main use of The algebraic method is generalized method; the second is the use of the geometric meanings of absolute value, by observing the number of axes to get the value of the function and the corresponding value of x, the starting point of this method is the shape - number