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高中数学集合与函数性质练习题

集合与函数的性质练习题 一、选择题(共 12 题,每题 5 分,共 60 分。 ) 1 、 U={1 , 2 , 3 , 4 , 5} , A={1,2,3} , B={2,5} BCAU ( ) A {2} B {2,3} C {3} D {1,3} 2、 若集合 A=}2{ xx, 3 a, 则下列结论中正确的是 ( )A Aa B Aa }{ C Aa }{ D Aa 3、函数 52)( xxf 的定义域是( ) A ),25( B ),25[ C )25,( D ]2 5,( 4、在区间(0,+≦)上不是增函数的函数是 ( ) A.y=2x+1 B.y=3x2+1 C.y= x 2 D.y=2x2+x+1 5、二次函数 542 mxxy 的对称轴为 2 x,则当 x=1 时,y 的值为( )A 7 B 1 C 17 D 25 6、已知函数 axxxf 2)(是偶函数,则当]2,1[ x 时,)(xf 的值域是: A.]4,1[ B.]4,0[ C.]4,4[ D.]2,0[ 7、某学生离家去学校,由于怕迟到,一开始就跑步,等跑累了再步行走完余下的路程,若 以纵轴表示离家的距离, 横轴表示离家后的时间, 则下列四个图形中, 符合该学生走法的是

8、函数 f(x)=4x2-mx+5 在[-2,+≦]上是增函数,在(-≦,-2)上是减函数,则 f(1) 等于( ) A.-7 B.1 C.17 D.25 9、集合 A=2{40}xxpx B=2{20}xxqx 2AB pq = A 2 B 3 C 4 D 5 10. 函数 f(x)= 2 1 xax 在区间(-2,+≦)上单调递增,则实数 a 的取值范围是 ( ) A.(0, 21)B.( 2 1 ,+≦)C.(-2,+≦)D.(-≦,-1)∪(1,+≦) 11、函数)2()(||)(xxxgxxf 区间依次是 ( )A. ]1,(],0,( B. ),1[],0,( C. ]1,(),,0[ D),1[),,0[ 12 2212fxxax 4, a 的取值范 围 ( ) A.a≤3 B.a≥-3 C.a≤5 D.a≥3 二、填空题(共 4 小题,每小题 5 分,共 20 分) 13、 集合}33|{ xxU, }11|{ xxM, }20|{ xxNCU, 那么 N , )(NCMU NM 14、下表是弹簧伸长的长度 d 与拉力 f 的相关数据

d/cm 1 2 3 4 5 f/N 14.2 28.8 41.3 57.5 70.2 根据表中的数据及它们的散点图, 写出一个基本能反映这一变化现象的函数解析式 15、已知 2(0) ()2(0) xxfxxx (1)f = ; 16、若 2()(2)(1)3fxkxkx )(xf 的减区间是_____________.



三、解答题(共 6 题,共 70 分) 17、已知集合{12},{213} AxxBxyxx BA ③()()RRCACB 12 分)

BA



18、对于二次函数 2 ()231fxxx 12 分) (1)写出它的单调区间; (2)求函数()fx 在[0,2]上的最大值及最小值; (3)当 x 分别取何值时,()0fx 。 19、集合}71{ xxA,集合}521{ axaxB,若满足 }73{ xxBA 实数 a 的值. 20、证明函数 f(x)=13 x 在[3,5]上单调递减,并求函数在[3,5]的最大值和 最小值。


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