給出下列命題(其中a>0且a≠1):
①函數(shù)y=ax-1與y=-ax+1的圖象關(guān)于原點(diǎn)對(duì)稱(chēng).
②函數(shù)y=ax-1與y=-ax+1的圖象關(guān)于x軸對(duì)稱(chēng).
③函數(shù)y=ax-2與y=a2-x的圖象關(guān)于y軸對(duì)稱(chēng).
④函數(shù)y=ax-2與y=a2-x的圖象關(guān)于x=2軸對(duì)稱(chēng).
⑤函數(shù)y=ax+2與y=a2-x的圖象關(guān)于y軸對(duì)稱(chēng).
其中正確的命題是 .
【答案】分析:根據(jù)圖象關(guān)于原點(diǎn)對(duì)稱(chēng)、圖象關(guān)于x軸對(duì)稱(chēng)、圖象關(guān)于y軸對(duì)稱(chēng)、圖象關(guān)于x=2軸對(duì)稱(chēng),分別寫(xiě)出各個(gè)函數(shù)圖象對(duì)稱(chēng)的函數(shù)圖象的解析式,再對(duì)照選項(xiàng)即可得出正確答案.
解答:解:對(duì)于命題(其中a>0且a≠1):
①∵函數(shù)y=ax-1與y=-a-x+1的圖象關(guān)于原點(diǎn)對(duì)稱(chēng).故①錯(cuò);
②∵函數(shù)y=ax-1與y=-ax+1的圖象關(guān)于x軸對(duì)稱(chēng).故②對(duì);
③∵函數(shù)y=ax-2與y=a-x-2的圖象關(guān)于y軸對(duì)稱(chēng).故③錯(cuò);
④∵函數(shù)y=ax-2與y=a2-x的圖象關(guān)于x=2軸對(duì)稱(chēng).故④對(duì);
⑤∵函數(shù)y=ax+2與y=a2-x的圖象關(guān)于y軸對(duì)稱(chēng).故⑤對(duì).
其中正確的命題是 ②④⑤.
故答案為:②④⑤.
點(diǎn)評(píng):本題主要考查函數(shù)的圖象的對(duì)稱(chēng)性的應(yīng)用,考查了命題的真假判斷與應(yīng)用,屬于基礎(chǔ)題.
科目:高中數(shù)學(xué)
來(lái)源:2012-2013學(xué)年四川省成都市武侯區(qū)玉林中學(xué)高一(上)期中數(shù)學(xué)試卷(解析版)
題型:填空題
給出下列命題(其中a>0且a≠1):
①函數(shù)y=ax-1與y=-ax+1的圖象關(guān)于原點(diǎn)對(duì)稱(chēng).
②函數(shù)y=ax-1與y=-ax+1的圖象關(guān)于x軸對(duì)稱(chēng).
③函數(shù)y=ax-2與y=a2-x的圖象關(guān)于y軸對(duì)稱(chēng).
④函數(shù)y=ax-2與y=a2-x的圖象關(guān)于x=2軸對(duì)稱(chēng).
⑤函數(shù)y=ax+2與y=a2-x的圖象關(guān)于y軸對(duì)稱(chēng).
其中正確的命題是 .
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