题目

1.将下列函数转换为分段函数形式.-|||-(1) =|x|+1;-|||-(2) =|x-2|;

$\begin{aligned} &1.将下列函数转换为分段函数形式.\\ &(1)y= \mid x \mid+ 1;\\ & (2)y= \mid x-2 \mid ; \end{aligned}$

题目解答

答案

$\begin{aligned} &(1)y=|x|+1= 1+\left \{ \begin{aligned} &x \ \ (x>0)\\ &-x\ \ (x\le 0) \end{aligned} \right. \\&=\left \{ \begin{aligned} &x +1\ \ (x>0)\\ &-x+1\ \ (x\le 0) \\ \end{aligned} \right.\\ &(2)y=|x-2|=\left \{ \begin{aligned} &x-2 \ \ (x>2)\\ &-(x-2)\ \ (x\le 2) \end{aligned} \right. \\&= \left \{ \begin{aligned} &x-2 \ \ (x>2)\\ &-x+2\ \ (x\le 2) \end{aligned} \right. \end{aligned}$