2018-2019学年高一数学上学期期中试题 (IV)

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1、2018-2019学年高一数学上学期期中试题(IV)一、选择题（本大题共12小题，每小题5分，每小题给出的四个选项中，只有一项符合要求）1、已知则()2、若函数则方程的解是()....3、方程的根所在区间是()....4、下列函数中，与是同一函数的是()5、若，，，则的大小关系是()6、函数恒过定点，则()7.已知函数是幂函数，则()8、函数在区间上是单调函数，则()9、函数使成立的的集合是()10、函数的图像大致是()11、若函数是奇函数，则使成立的的取值范围是()12、某同学在研究函数时，分别给出下面几个结论：①函数是奇函数；②函数的值域为；③函数在上是增函数；其

2、中正确结论的序号是()①②③①③②③①②二、填空题（本大题共4小题，每小题5分）13、设集合___________.14、定义在上的函数是奇函数且每隔2个单位的函数值都相等,则_____________.15、已知集合_____________.16、已知函数是定义在上的偶函数，当时，，如果函数恰有个零点，则实数的取值范围是　　　　．三、解答题（本大题6小题，共70分，解答应写出必要的文字说明，证明过程或演算步骤）17、(本小题10分)(1)已知函数，求的定义域；(2)解不等式18、(本小题12分)已知集合(1)求与.(2)若求实数的取值范围.19、(本小题12分)已

3、知函数(1)求函数的定义域；(2)判断函数在定义域上的单调性，并说明理由；(3)当满足什么关系时,在上恒取正值.20、(本小题12分)已知:函数（且）.(1)求函数的定义域;(2)判断函数的奇偶性,并加以证明;(3)设,解不等式.21、(本小题12分)求函数的单调区间(写出解答过程)22、(本小题12分)已知函数对一切实数都满足,且.(1)求的值；(2)求的解析式；(3)当时，恒成立，求的范围．2021届高一上学期期中考试答案一、选择题题号123456789101112答案CADABCDCBDDA二、填空题题号13141516答案三、解答题17、（本小题满分10分）解

4、析：(1)由条件可知，······································2分函数在上单调递增·····················································3分.···························································5分(2)··················································7分又函数在上单调递减，·····················9分·······················

5、·················10分18．（本小题满分12分）解析：(1)由条件可知································3分又.····························································4分·············································6分(2)··············································8分分析可知，解得········································

6、10分·····································································12分19．（本小题满分12分）解析：(1),················································1分又，·····································································2分定义域为.································································

7、··3分(2)函数在定义域上是单调递增函数.证明：，················4分··································································6分·························································7分所以函数在定义域上是单调递增函数.···································8分(3)要使得在上恒为正值，则在上的最小值必须大于0，由(2)知······················