Question

1．函數(shù)y=|x-1|+1可表示為（　�。�

• A． $y=\left\{{\begin{array}{l}{2-x，x＜1}\\{x，x＞1}\end{array}}\right.$
• B． $y=\left\{{\begin{array}{l}{2-x，x＞1}\\{x，x≤1}\end{array}}\right.$
• C． $y=\left\{{\begin{array}{l}{x，x＜1}\\{2-x，x≥1}\end{array}}\right.$
• D． $y=\left\{{\begin{array}{l}{2-x，x＜1}\\{x，x≥1}\end{array}}\right.$

Answer 1

分析 對(duì)x-1與0的大小進(jìn)行分段討論去絕對(duì)值，可得答案．

解答 解：函數(shù)y=|x-1|+1，
當(dāng)x-1＞0，即x≥1時(shí)，y=x-1+1=x．
當(dāng)x-1＜0，即x＜1時(shí)，y=-x+1+1=2-x．
∴得y=$\left\{\begin{array}{l}{x，x≥1}\\{2-x，x＜1}\end{array}\right.$，
故選D．

點(diǎn)評(píng) 本題考查了討論思想去絕對(duì)值求解分段函數(shù)的解析式的問(wèn)題．比較基礎(chǔ)題．