Question

已知：點A（x₁，y₁）、B（x₂，y₂）、C（x₃，y₃）是函數y=﹣圖象上的三點，且x₁＜0＜x₂＜x₃則y₁、y₂、y₃的大小關系是（　　）                                                                                        

A．y₁＜y₂＜y₃              B．y₂＜y₃＜y₁              C．y₃＜y₂＜y₁              D．無法確定

Answer 1

B【考點】反比例函數圖象上點的坐標特征．                                           

【專題】壓軸題．                                                                              

【分析】對y=﹣，由x₁＜0＜x₂＜x₃知，A點位于第二象限，y₁最大，第四象限，y隨x增大而增大，y₂＜y₃，故y₂＜y₃＜y₁．                                                                                                   

【解答】解：∵y=﹣中k=﹣3＜0，                                                       

∴此函數的圖象在二、四象限，                                                              

∵點A（x₁，y₁）、B（x₂，y₂）、C（x₃，y₃）是函數y=﹣圖象上的三點，且x₁＜0＜x₂＜x₃，               

∴A點位于第二象限，y₁＞0，B、C兩點位于第四象限，                                

∵0＜x₂＜x₃，                                                                                    

∴y₂＜y₃，                                                                                         

∴y₂＜y₃＜y₁．                                                                                   

故選B．                                                                                            

【點評】本題考查了反比例函數圖象上點的坐標特征，要學會比較圖象上點的坐標．