2018-2019學(xué)年高一數(shù)學(xué) 寒假作業(yè)(6)冪函數(shù) 新人教A版.doc
高一數(shù)學(xué)寒假作業(yè)(6)冪函數(shù)1、已知冪函數(shù),當(dāng)時(shí)為減函數(shù),則( )A. B. C. 或D. 2、下列函數(shù)在其定義域內(nèi)既是奇函數(shù)又是增函數(shù)的是( )A. B. C. D. 3、已知冪函數(shù)是有理數(shù))的圖象過點(diǎn),則的單調(diào)遞減區(qū)間是( )A. B. C. D. 4、函數(shù)在區(qū)間上的最大值是()A. B. C. D. 5、函數(shù)的圖象是( )A. B.C.D.6、下列結(jié)論中,正確的是( )A.冪函數(shù)的圖象都經(jīng)過點(diǎn)B.冪函數(shù)的圖象不可能出現(xiàn)在第四象限C.當(dāng)冪指數(shù)取時(shí),冪函數(shù)是增函數(shù)D.當(dāng)冪指數(shù)時(shí),冪函數(shù)是減函數(shù)7、下列函數(shù)中,是冪函數(shù)的是( )A. B. C. D. 8、下列函數(shù)既是偶函數(shù)又是冪函數(shù)的是( )A. B. C. D. 9、已知冪函數(shù)是偶函數(shù),則實(shí)數(shù)的值是( )A. B. C. D. 或10、設(shè),則的大小關(guān)系是( )A. B. C. D. 11、已知冪函數(shù)的圖象經(jīng)過點(diǎn),則的值為_.12、已知冪函數(shù)的圖象不經(jīng)過原點(diǎn),則_.13、若函數(shù)是偶函數(shù),且在內(nèi)是減函數(shù).則整數(shù)的所有可能值為_.14、已知冪函數(shù)的圖象經(jīng)過點(diǎn),點(diǎn)在冪函數(shù)的圖象上.1.求的解析式.2.當(dāng)為何值時(shí),當(dāng)為何值時(shí), 15、已知函數(shù).1.若函數(shù)為奇函數(shù),求實(shí)數(shù)的值;2.若對(duì)任意的都有成立,求實(shí)數(shù)的取值范圍. 答案以及解析1答案及解析:答案:A解析:因?yàn)闉閮绾瘮?shù),解得或因?yàn)楫?dāng)時(shí), 為減函數(shù),解得所以的值為2. 2答案及解析:答案:C解析: 3答案及解析:答案:B解析:的圖像過點(diǎn).,.,的單調(diào)遞增區(qū)間為. 4答案及解析:答案:C解析:由冪函數(shù)的性質(zhì),可知當(dāng)時(shí), 在上是減函數(shù),故在區(qū)間上是減函數(shù),故. 5答案及解析:答案:A解析:因?yàn)閳D象必過點(diǎn),且關(guān)于軸對(duì)稱.所以C、D 不正確.因?yàn)楫?dāng)時(shí), 的值隨的增大而增大,且增大的速度越來(lái)越快,所以B不正確.故選A. 6答案及解析:答案:B解析:當(dāng)冪指數(shù)時(shí).冪函數(shù)的圖象不經(jīng)過原點(diǎn),故A錯(cuò)誤;因?yàn)樵谥?,只?必有,所以冪函數(shù)的圖象不可能在第四象限.故B正確;當(dāng)時(shí).冪函數(shù)在上遞減,在上遞增,故C錯(cuò)誤;當(dāng)時(shí),冪函數(shù)在整個(gè)定義域上不是減函數(shù).故D錯(cuò)誤.故選B. 7答案及解析:答案:C解析: 8答案及解析:答案:B解析:對(duì)于A,函數(shù)是奇函數(shù),不合題意;對(duì)于B,函數(shù)是偶函數(shù)且是冪函數(shù),符合題意;對(duì)于C:,函數(shù)不是偶函數(shù),不合題意;對(duì)于D,函數(shù)不是冪函數(shù),不合題意.故選B 9答案及解析:答案:A解析:已知函數(shù)是冪函數(shù),則,解得或,當(dāng)時(shí), 不是偶函數(shù);當(dāng)時(shí), 是偶函數(shù).綜上,實(shí)數(shù)的值是,故選A 10答案及解析:答案:A解析:指數(shù)函數(shù)單調(diào)遞減,即. 冪函數(shù)在上單調(diào)遞增,即,故選A 11答案及解析:答案:4解析:設(shè),因?yàn)楹瘮?shù)的圖象經(jīng)過點(diǎn), 12答案及解析:答案:1或2解析:為冪函數(shù).或.當(dāng)時(shí), ,其圖像不經(jīng)過原點(diǎn),符合題意;當(dāng)時(shí), ,其圖像不經(jīng)過原點(diǎn),也符合題意.m的值為1或2. 13答案及解析:答案:解析:由題意知應(yīng)為負(fù)偶數(shù),即.當(dāng)時(shí), 或;當(dāng)時(shí), 或. 14答案及解析:答案:1.設(shè)則設(shè)則2.當(dāng)或時(shí), 當(dāng)或時(shí), 解析: 15答案及解析:答案:1.是奇函數(shù),即,對(duì)一切恒成立,.2.對(duì)于,均有,即成立,對(duì)恒成立.,又在上單調(diào)遞增,當(dāng)時(shí), ,.解析: