Question

函數(shù)y=-e^x的圖象（ ）
A．與y=e^x的圖象關(guān)于y軸對(duì)稱(chēng)
B．與y=e^x的圖象關(guān)于坐標(biāo)原點(diǎn)對(duì)稱(chēng)
C．與y=e^-x的圖象關(guān)于y軸對(duì)稱(chēng)
D．與y=e^-x的圖象關(guān)于坐標(biāo)原點(diǎn)對(duì)稱(chēng)

Answer 1

【答案】分析：函數(shù)圖象的對(duì)稱(chēng)問(wèn)題，往往轉(zhuǎn)化為點(diǎn)的對(duì)稱(chēng)問(wèn)題．函數(shù)y=-e^x與y=e^xx相同時(shí)，y互為相反數(shù)，故可考慮點(diǎn)（x，y）和點(diǎn)（x，-y）的對(duì)稱(chēng)問(wèn)題；同理y=-e^x的圖象與y=e^-x的圖象的對(duì)稱(chēng)問(wèn)題考慮點(diǎn)（x，y）和點(diǎn)（-x，-y）的對(duì)稱(chēng)．
解答：解：因?yàn)辄c(diǎn)（x，y）和點(diǎn)（x，-y）關(guān)于x軸對(duì)稱(chēng)，所以y=-e^x的圖象與y=e^x的圖象關(guān)于x軸對(duì)稱(chēng)，故A和B錯(cuò)誤；
因?yàn)辄c(diǎn)（x，y）和點(diǎn)（-x，-y）關(guān)于原點(diǎn)對(duì)稱(chēng)，所以y=-e^x的圖象與y=e^-x的圖象關(guān)于坐標(biāo)原點(diǎn)對(duì)稱(chēng)
故選D
點(diǎn)評(píng)：本題考查函數(shù)圖象的對(duì)稱(chēng)問(wèn)題，函數(shù)圖象的對(duì)稱(chēng)問(wèn)題，往往轉(zhuǎn)化為點(diǎn)的對(duì)稱(chēng)問(wèn)題處理．