新高考数学一轮复习 函数专项重难点突破专题06 函数的单调性(原卷版)

专题06函数的单调性真题再现一、单选题1．（2023·北京·统考高考真题）下列函数中，在区间SKIPIF1<0上单调递增的是（

）A．SKIPIF1<0B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2023·全国·统考高考真题）设函数SKIPIF1<0在区间SKIPIF1<0上单调递减，则SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2023·全国·统考高考真题）已知函数SKIPIF1<0．记SKIPIF1<0，则（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·天津·统考高考真题）函数SKIPIF1<0的图像为（

）A． B．C． D．5．（2021·全国·高考真题）下列函数中是增函数的为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0考点一判断或证明函数的单调性一、单选题1．下列函数中，在区间SKIPIF1<0上为增函数的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．下列函数中，是奇函数且在区间SKIPIF1<0上单调递增的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．在下列函数中：①SKIPIF1<0，②SKIPIF1<0，③SKIPIF1<0，④SKIPIF1<0，在SKIPIF1<0上为增函数的有（

）A．①② B．③④ C．②③ D．①④二、解答题4．已知定义在SKIPIF1<0上的函数SKIPIF1<0是奇函数.(1)求实数SKIPIF1<0，SKIPIF1<0的值；(2)判断SKIPIF1<0在SKIPIF1<0上的单调性并用定义证明；(3)若对任意的SKIPIF1<0，不等式SKIPIF1<0恒成立，求实数SKIPIF1<0的取值范围.5．已知函数SKIPIF1<0在SKIPIF1<0为奇函数，且SKIPIF1<0(1)求SKIPIF1<0值；(2)判断函数SKIPIF1<0在SKIPIF1<0的单调性，并用定义证明；(3)解关于t的不等式SKIPIF1<06．已知函数SKIPIF1<0的定义域是SKIPIF1<0，满足SKIPIF1<0，SKIPIF1<0时SKIPIF1<0，对任意正实数x，y，都有SKIPIF1<0．(1)求SKIPIF1<0的值；(2)证明：函数SKIPIF1<0在SKIPIF1<0上是增函数；(3)求不等式SKIPIF1<0的解集．7．函数SKIPIF1<0是定义在SKIPIF1<0上的函数，满足下列条件：①SKIPIF1<0；②SKIPIF1<0；③任意SKIPIF1<0，有SKIPIF1<0．(1)求SKIPIF1<0的值；(2)判断并证明函数SKIPIF1<0在区间SKIPIF1<0上的单调性；(3)解不等式SKIPIF1<0．考点二求单调性区间一、单选题1．函数SKIPIF1<0的单调递减区间为（

）A．（–∞，2] B．[2，+∞）C．[0，2] D．[0，+∞）2．函数SKIPIF1<0的单调递增区间是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．函数SKIPIF1<0的单调递增区间是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．函数SKIPIF1<0的单调递增区间为（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．函数SKIPIF1<0的单调递增区间是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．已知函数SKIPIF1<0若SKIPIF1<0，则SKIPIF1<0的单调递增区间为（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<07．函数SKIPIF1<0的单调递增区间是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．函数SKIPIF1<0的单调递减区间是（

）A．SKIPIF1<0 B．SKIPIF1<0和SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0和SKIPIF1<0二、填空题9．函数SKIPIF1<0的单调增区间为___________.10．函数SKIPIF1<0的单调递增区间是________11．若函数SKIPIF1<0是偶函数，则SKIPIF1<0的单调递增区间是__________．12．函数SKIPIF1<0的单调递减区间是________．13．函数SKIPIF1<0的单调递增区间为__________.三、双空题14．函数SKIPIF1<0的单调增区间是_______；函数SKIPIF1<0的单调增区间是_______四、解答题15．已知函数SKIPIF1<0为定义在SKIPIF1<0上的偶函数，其部分图象如图所示.(1)请作出函数SKIPIF1<0在SKIPIF1<0上的图象；(2)根据函数图象写出函数SKIPIF1<0的单调区间及最值.16．已知函数SKIPIF1<0．(1)当SKIPIF1<0时，求函数SKIPIF1<0的单调区间；(2)若SKIPIF1<0在SKIPIF1<0上单调递减，求a的取值范围．考点三图像与单调性一、单选题1．已知函数SKIPIF1<0的图象如图所示，则下列说法错误的是（

）

A．SKIPIF1<0是函数SKIPIF1<0的增区间 B．SKIPIF1<0是函数SKIPIF1<0的减区间C．函数SKIPIF1<0在SKIPIF1<0上是增函数 D．函数SKIPIF1<0在SKIPIF1<0上是减函数二、多选题2．函数SKIPIF1<0是定义在SKIPIF1<0上的偶函数，SKIPIF1<0在SKIPIF1<0上的图象如图所示，则函数SKIPIF1<0的增区间是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．奇函数SKIPIF1<0在SKIPIF1<0的图像如图所示，则下列结论正确的有（

）A．当SKIPIF1<0时，SKIPIF1<0B．函数SKIPIF1<0在SKIPIF1<0上递减C．SKIPIF1<0D．函数SKIPIF1<0在SKIPIF1<0上递增4．设SKIPIF1<0是定义域为SKIPIF1<0的偶函数，其导函数为SKIPIF1<0，若SKIPIF1<0时，SKIPIF1<0图像如图所示，则可以使SKIPIF1<0成立的SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0三、解答题5．已知函数SKIPIF1<0.(1)在下面的平面直角坐标系中，作出函数SKIPIF1<0的图象，并写出单调增区间；(2)方程SKIPIF1<0有四个不相等的实数根，求实数SKIPIF1<0的取值范围.6．给定函数SKIPIF1<0，SKIPIF1<0，SKIPIF1<0.(1)在同一直角坐标系中画出函数SKIPIF1<0和SKIPIF1<0的图象；(2)SKIPIF1<0，用SKIPIF1<0表示SKIPIF1<0，SKIPIF1<0中的最大者，记为SKIPIF1<0，试判断SKIPIF1<0在区间SKIPIF1<0的单调性.7．已知函数SKIPIF1<0是定义在SKIPIF1<0上的偶函数，当SKIPIF1<0时，SKIPIF1<0.现已画出函数SKIPIF1<0在SKIPIF1<0轴左侧的图像，如图所示.(1)画出函数SKIPIF1<0在y轴右侧的图像，并写出函数SKIPIF1<0在SKIPIF1<0上的单调增区间；(2)求函数SKIPIF1<0在SKIPIF1<0上的解析式.(3)结合图像分别直接写出：当m为何值时，关于x的方程SKIPIF1<0有4个实根？考点四根据单调性比较大小一、单选题1．已知函数SKIPIF1<0是区间SKIPIF1<0内的减函数，则SKIPIF1<0与SKIPIF1<0的大小关系为（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．不确定2．设函数SKIPIF1<0满足：对任意的SKIPIF1<0都有SKIPIF1<0，则SKIPIF1<0与SKIPIF1<0大小关系是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0的大小关系为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．已知SKIPIF1<0是偶函数，SKIPIF1<0在SKIPIF1<0上是增函数，则SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的大小关系为：（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．已知SKIPIF1<0，则SKIPIF1<0的大小关系为（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．已知函数SKIPIF1<0，设SKIPIF1<0，则（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知函数SKIPIF1<0在SKIPIF1<0上是递减函数，SKIPIF1<0且SKIPIF1<0，则有（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<08．已知函数SKIPIF1<0．记SKIPIF1<0，则（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．设SKIPIF1<0为定义在SKIPIF1<0上的偶函数，且SKIPIF1<0在SKIPIF1<0上为增函数，则SKIPIF1<0的大小顺序为（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<010．已知函数SKIPIF1<0是定义在SKIPIF1<0上的偶函数，函数SKIPIF1<0是定义在SKIPIF1<0上的奇函数，且SKIPIF1<0，SKIPIF1<0在SKIPIF1<0上单调递减，则（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<011．已知函数SKIPIF1<0的定义域为SKIPIF1<0，若对SKIPIF1<0都有SKIPIF1<0，且SKIPIF1<0在SKIPIF1<0上单调递减，则SKIPIF1<0与SKIPIF1<0的大小关系是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<012．设SKIPIF1<0，则SKIPIF1<0大小关系是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<013．设SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，则（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<014．已知SKIPIF1<0且SKIPIF1<0，SKIPIF1<0且SKIPIF1<0，SKIPIF1<0且SKIPIF1<0，则（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多选题15．已知函数SKIPIF1<0是其导函数，恒有SKIPIF1<0，则下列结论正确的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0三、填空题16．若函数SKIPIF1<0在SKIPIF1<0上是偶函数，SKIPIF1<0在SKIPIF1<0上单调递增，则SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的大小关系是___________.考点五根据单调性解不等式一、多选题1．若函数SKIPIF1<0在SKIPIF1<0上为减函数，且SKIPIF1<0，则实数SKIPIF1<0的值可以是（

）A．1 B．2 C．3 D．42．已知函数SKIPIF1<0，且满足SKIPIF1<0，则实数SKIPIF1<0的取值可能为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．1 D．2二、单选题3．已知函数SKIPIF1<0，不等式SKIPIF1<0的解集为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．函数SKIPIF1<0是定义在SKIPIF1<0上的增函数，则满足SKIPIF1<0的SKIPIF1<0的取值范围是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．已知奇函数SKIPIF1<0是定义在区间SKIPIF1<0上的增函数，且SKIPIF1<0，则实数SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知偶函数SKIPIF1<0，则满足SKIPIF1<0的实数SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知定义在SKIPIF1<0上的偶函数SKIPIF1<0在SKIPIF1<0上是增函数，且SKIPIF1<0，则使SKIPIF1<0的SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．设奇函数SKIPIF1<0在SKIPIF1<0上为单调递增函数，且SKIPIF1<0，则不等式SKIPIF1<0，的解集为（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<09．已知定义在SKIPIF1<0上的函数SKIPIF1<0在SKIPIF1<0上单调递减，且SKIPIF1<0为偶函数，则不等式SKIPIF1<0的解集为（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<010．已知函数SKIPIF1<0对任意的SKIPIF1<0，都有SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0，则不等式SKIPIF1<0的解集为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．设函数SKIPIF1<0，若SKIPIF1<0，则实数a的范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0三、填空题12．已知函数SKIPIF1<0是SKIPIF1<0上的奇函数，函数SKIPIF1<0在SKIPIF1<0上单调递减，SKIPIF1<0，则不等式SKIPIF1<0的解集是___________.13．已知函数SKIPIF1<0，则使得SKIPIF1<0成立的SKIPIF1<0的取值范围是___________.四、解答题14．已知函数SKIPIF1<0是定义在SKIPIF1<0上的奇函数，当SKIPIF1<0时，SKIPIF1<0.(1)求当SKIPIF1<0时，函数SKIPIF1<0的解析式；(2)若SKIPIF1<0，求实数SKIPIF1<0的取值范围.15．若非零函数SKIPIF1<0对任意实数a，b，均有SKIPIF1<0，且当SKIPIF1<0时，SKIPIF1<0．(1)求SKIPIF1<0的值．(2)求证：①任意SKIPIF1<0，SKIPIF1<0．②SKIPIF1<0为减函数．(3)当SKIPIF1<0时，解不等式SKIPIF1<0．(4)若SKIPIF1<0，求SKIPIF1<0在SKIPIF1<0上的最大值和最小值．考点六根据单调性求参一、单选题1．函数SKIPIF1<0在SKIPIF1<0上是减函数，则（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．已知二次函数SKIPIF1<0在区间SKIPIF1<0内是单调函数，则实数SKIPIF1<0的取值范围是（

）A．SKIPIF1<0或SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<03．若函数SKIPIF1<0的单调减区间是SKIPIF1<0，则（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．已知函数SKIPIF1<0在R上单调递增，则实数a的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．已知函数SKIPIF1<0在SKIPIF1<0上单调递增，则实数a的取值范围为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知函数SKIPIF1<0若SKIPIF1<0在SKIPIF1<0上单调递减，则实数SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知函数SKIPIF1<0在区间SKIPIF1<0上是单调函数，则SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．已知函数SKIPIF1<0在SKIPIF1<0上是减函数，则实数SKIPIF1<0