Question

已知：点A（x₁，y₁）、B（x₂，y₂）、C（x₃，y₃）是函数y=﹣图象上的三点，且x₁＜0＜x₂＜x₃则y₁、y₂、y₃的大小关系是（　　）                                                                                        

A．y₁＜y₂＜y₃              B．y₂＜y₃＜y₁              C．y₃＜y₂＜y₁              D．无法确定

Answer 1

B【考点】反比例函数图象上点的坐标特征．                                           

【专题】压轴题．                                                                              

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

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

∴此函数的图象在二、四象限，                                                              

∵点A（x₁，y₁）、B（x₂，y₂）、C（x₃，y₃）是函数y=﹣图象上的三点，且x₁＜0＜x₂＜x₃，               

∴A点位于第二象限，y₁＞0，B、C两点位于第四象限，                                

∵0＜x₂＜x₃，                                                                                    

∴y₂＜y₃，                                                                                         

∴y₂＜y₃＜y₁．                                                                                   

故选B．                                                                                            

【点评】本题考查了反比例函数图象上点的坐标特征，要学会比较图象上点的坐标．