新高考数学一轮复习 函数专项重难点突破专题05 分段函数(原卷版)

专题05分段函数真题再现1．（2023·北京·统考高考真题）设SKIPIF1<0，函数SKIPIF1<0，给出下列四个结论：①SKIPIF1<0在区间SKIPIF1<0上单调递减；②当SKIPIF1<0时，SKIPIF1<0存在最大值；③设SKIPIF1<0，则SKIPIF1<0；④设SKIPIF1<0．若SKIPIF1<0存在最小值，则a的取值范围是SKIPIF1<0．其中所有正确结论的序号是____________．2．（2022·浙江·统考高考真题）已知函数SKIPIF1<0则SKIPIF1<0________；若当SKIPIF1<0时，SKIPIF1<0，则SKIPIF1<0的最大值是_________．3．（2022·北京·统考高考真题）设函数SKIPIF1<0若SKIPIF1<0存在最小值，则a的一个取值为________；a的最大值为___________．4．（2021·浙江·统考高考真题）已知SKIPIF1<0，函数SKIPIF1<0若SKIPIF1<0，则SKIPIF1<0___________.考点一分段函数函数值(解析式)一、单选题1．已知函数SKIPIF1<0，则SKIPIF1<0（

）A．5B．3 C．2 D．12．已知函数SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．1 C．-1 D．23．已知函数SKIPIF1<0，则SKIPIF1<0（

）A．4 B．8 C．16 D．324．已知函数SKIPIF1<0，若SKIPIF1<0，则SKIPIF1<0（）.A．SKIPIF1<01 B．SKIPIF1<02 C．SKIPIF1<03 D．SKIPIF1<045．已知函数SKIPIF1<0，则SKIPIF1<0的值为（

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

）A．4 B．5 C．6 D．77．已知函数SKIPIF1<0，则SKIPIF1<0（

）A．1 B．e C．SKIPIF1<0 D．SKIPIF1<08．若函数SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多选题9．函数f(x)的图象如图所示，则f(x)的解析式是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0三、填空题10．已知函数SKIPIF1<0，则SKIPIF1<0___________．11．已知函数SKIPIF1<0，则SKIPIF1<0___________．12．已知函数SKIPIF1<0，则SKIPIF1<0_________．13．设函数SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0的解析式为____________．14．设SKIPIF1<0定义在SKIPIF1<0上且SKIPIF1<0，则SKIPIF1<0______．考点二分段函数定义域和值域一、单选题1．设函数SKIPIF1<0，SKIPIF1<0则SKIPIF1<0的值域是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．若定义运算SKIPIF1<0，则函数SKIPIF1<0的值域是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多选题3．已知函数SKIPIF1<0，关于函数SKIPIF1<0的结论正确的是（

）A．SKIPIF1<0的定义域是R B．SKIPIF1<0的值域是SKIPIF1<0C．若SKIPIF1<0，则x的值为SKIPIF1<0 D．SKIPIF1<0三、填空题4．函数SKIPIF1<0的定义域是________.5．已知SKIPIF1<0，则SKIPIF1<0的值域是______；6．函数SKIPIF1<0的值域是______．7．已知函数SKIPIF1<0SKIPIF1<0的最大值为m，SKIPIF1<0的最小值为n，则SKIPIF1<0______．8．已知函数SKIPIF1<0，则SKIPIF1<0的最小值为_________．四、双空题9．函数y＝SKIPIF1<0的定义域为________，值域为________.10．如图为一分段函数的图象，则该函数的定义域为________，值域为________．五、解答题11．已知函数SKIPIF1<0的图象如图所示，其中SKIPIF1<0轴的左侧为一条线段，右侧为某抛物线的一段．(1)写出函数SKIPIF1<0的定义域和值域；(2)求SKIPIF1<0的值．考点三分段函数单调性一、单选题1．定义运算：SKIPIF1<0，例如：SKIPIF1<0，SKIPIF1<0，则函数SKIPIF1<0的单调递增区间为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．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<03．若函数SKIPIF1<0是SKIPIF1<0上的单调函数，则实数SKIPIF1<0的取值范围为（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0二、多选题4．已知函数SKIPIF1<0在R上单调递增，则实数a的取值可以是（

）A．0 B．1 C．2 D．3三、填空题5．设函数SKIPIF1<0，SKIPIF1<0，则函数SKIPIF1<0的递增区间为________.6．函数SKIPIF1<0的单调增区间为__________.7．己知函数SKIPIF1<0满足对任意SKIPIF1<0，且SKIPIF1<0，都有SKIPIF1<0成立，则实数a的取值范围是__________．8．已知函数SKIPIF1<0，设SKIPIF1<0，若SKIPIF1<0，则SKIPIF1<0的取值范围是____________.四、双空题9．函数SKIPIF1<0的单调性为______；奇偶性为______．五、解答题10．已知函数SKIPIF1<0(1)求SKIPIF1<0，SKIPIF1<0的值；(2)若SKIPIF1<0，求实数a的值；(3)直接写出SKIPIF1<0的单调区间．考点四分段函数求参一、单选题1．已知函数SKIPIF1<0，若SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．0 C．1 D．22．设SKIPIF1<0，若SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．0 C．1 D．23．已知函数SKIPIF1<0SKIPIF1<0的值域为SKIPIF1<0，则实数SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．已知函数SKIPIF1<0的最大值为0，则实数a的取值范围为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．若函数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<06．已知函数SKIPIF1<0，满足对任意的实数SKIPIF1<0，SKIPIF1<0且SKIPIF1<0，都有SKIPIF1<0，则实数a的取值范围为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知函数SKIPIF1<0在SKIPIF1<0是减函数，则实数SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．函数SKIPIF1<0，若SKIPIF1<0互不相等，且SKIPIF1<0，则SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、填空题9．已知SKIPIF1<0，函数SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0________．10．已知函数SKIPIF1<0．若SKIPIF1<0，则实数m的取值范围是______．11．设函数SKIPIF1<0，若SKIPIF1<0，则实数a＝_____．12．已知函数SKIPIF1<0且SKIPIF1<0，则正数SKIPIF1<0的值为______.13．设函数SKIPIF1<0存在最小值，则SKIPIF1<0的取值范围是________.14．已知SKIPIF1<0，若存在三个不同实数SKIPIF1<0使得SKIPIF1<0，则SKIPIF1<0的取值范围是______．15．设SKIPIF1<0且SKIPIF1<0，已知数列SKIPIF1<0满足SKIPIF1<0，且SKIPIF1<0是递增数列，则a的取值范围是____．16．已知SKIPIF1<0，其中SKIPIF1<0且SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0___________．考点五解分段函数不等式一、单选题1．已知SKIPIF1<0,则使SKIPIF1<0成立的SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．已知函数SKIPIF1<0，则满足不等式SKIPIF1<0的x的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．已知函数SKIPIF1<0，若SKIPIF1<0，则实数a的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．已知函数SKIPIF1<0，则不等式SKIPIF1<0的解集是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．若SKIPIF1<0，且SKIPIF1<0的解集为SKIPIF1<0，则SKIPIF1<0的取值范围是（

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

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0二、多选题7．已知SKIPIF1<0是定义在SKIPIF1<0的奇函数，且SKIPIF1<0时，SKIPIF1<0，则下列结论正确的是（

）A．SKIPIF1<0时，SKIPIF1