Question

給出下列五種說(shuō)法：函數(shù) (k∈Z)是奇函數(shù)
函數(shù)的圖象關(guān)于點(diǎn) (k∈Z)對(duì)稱(chēng)；
③函數(shù)的最小值為.
④
⑤函數(shù)在定義域上有一個(gè)零點(diǎn); 其中正確的是              (填序號(hào)).

Answer 1

②③④

試題分析：說(shuō)法①中函數(shù)可化為,則函數(shù)為偶函數(shù),故說(shuō)法①錯(cuò);說(shuō)法②中由函數(shù)的圖像可知關(guān)于點(diǎn)對(duì)稱(chēng),故說(shuō)法②正確;說(shuō)法③中函數(shù)可化為,令,則,所以當(dāng)時(shí),函數(shù),故說(shuō)法③正確;說(shuō)法④中,因?yàn)?img src="http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240319559012073.png" style="vertical-align:middle;" />,
又,即,
所以,
則,
同理,…, .
所以.故說(shuō)法④正確;說(shuō)法⑤中可轉(zhuǎn)化為函數(shù)與函數(shù)的交點(diǎn)個(gè)數(shù),當(dāng)時(shí),,由圖像可知此時(shí)函數(shù)與有三個(gè)交點(diǎn),故說(shuō)法⑤錯(cuò).所以正確的說(shuō)法有②③④.