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泸溪一中上学期期末复习试题高一数学


泸溪一中上学期高一数学练习题(函数) 1.已知全集 U ? ?0, ?1, ?2, ?3, ?4?, 集合 M ? ?0, ?1, ?2?, N ? ?0, ?3, ?4?, 那么 (CU M ) ? N = A. {0} B. {?3, ?4} C. {?1, ?2} D. ? 2.下列各组函数中,表示同一函数的是 ( ) A. y ? C. y ?

则 x0 y 0 与集合 M , N 的关系是 A. x0 y 0 ?M 但 ? N B. x0 y 0 ? N 但 ? M C. x 0 y 0 ? M 且 ? N D. x 0 y 0 ? M 且 ? N .

9. 设 U ? 2,3, a 2 ? a ? 1

?

?

A ? ?2,3?, 若 CU A ? ?? 1 ,则 a ?

x2 ?1 与 y ? x ?1 x ?1

B. D.

y ? lg x 与 y ?

1 lg x 2 2

10. 设 ? ? ?? 1,1, 1 ,3? ,则使函数 ? ? 2 ? ? 11.函数 y ? x2 ? 4x ,其中 x ? ) 12. 设集合 A ? {x | 2 x 2 13. 函数

y ? x ? 的定义域为 R 且为奇函数的所有 ? 的值_____.


x2 ?1 与 y ? x ? 1

y ? x 与 y ? log x a x (a > 0且a ? 1)


??3,3? ,则该函数的值域为

3.三个数 60.7 ,0.76 ,log0.7 6 的大小关系是

则实数 m 的取值_____。 ? 5x ? 3 ? 0} ,B ? {x | m x ? 1} 且 B ? A, .

A. 0.76 ? log0.7 6 ? 60.7 B. 0.76 ? 60.7 ? log0.7 6 C. log0.7 6 ? 60.7 ? 0.76 D. log0.7 6 ? 0.76 ? 60.7 4. 设函数 f ( x) ? 3x ? 3x ? 8 ,可得 f (1) ? 0, f (2) ? 0, f (1.5) ? 0, f (1.25) ? 0 .用二分法求方 程 3x ? 3x ? 8 ? 0 在 x ? (1, 2) 内的近似解,则方程的根所在的区间是 A. (1,1. 25) B. (1. 25,1. 5) C. (1. 5,2) ( )

且 f ( x) ? x ? 1, x ? 0 , 则当 x ? 0 ,f ( x) ? f ( x) 在 R 上为偶函数,

14.若幂函数

f ( x) ? (2m2 ? 5m ? 3) x 2m ?9m?9 在(0,+∞)上是减函数,则 m =
3 ? ax (a ? 1) a ?1

2

15. 已知函数 f ( x) ?

D. 不能确定

5. 设偶函数 f(x)的定义域为 R,当 x ? [0,??] 时 f(x)是增函数,则 f(-2),f( ? ),f(-3)的大 小关系是 A. f (? ) > f (?3) > f (?2) C. f (? ) < f (?3) < f (?2) 6. 已知 y
2

①若 a ? 0 ,则 f ( x) 的定义域为______________ ②若

( B. f (? ) > f (?2) > f (?3) D. f (? ) < f (?2) < f (?3) (



f ( x) 在区间 ?0,1? 上为 x 的减函数,则 a 的范围是____

16. 某池塘中野生水葫芦的面积与时间的函数关系的图象,如右图所示. 假设其关系为指数函 数,并给出下列说法: ) 错误!未找到引用源。此指数函数的底数为 2; 错误!未找到引用源。在第 5 个月时,野生水葫芦的面积就会 超过 30m ; 错误!未找到引用源。野生水葫芦从 4m 蔓延到 12m 只需 1.5 , 那么 (
2 2 2

? ax ? 2(a ? 2) x ? 5 在区间 (4, ??) 上是减函数,则 a 的范围是
B. a ? 2 C. a ?

A. a ? 2

5

5

2 a?0 或 5

D. a

?0
f ( x) 与 g ( x)
)

7. 已知 f ( x) ? a x ,g ( x) ? log a 在同一坐标系内的图像可能是

若 f( 3 )( 3 g ) 0< x(a > 0且a ? 1) ,

个月; 错 误 ! 未 找 到 引 用 源 。 设 野 生 水 葫 芦 蔓 延 到 2m ,3m , 6m 所 需 的 时 间 分 别 为 t1, t2, t3, 则有 t1 + t2 = t3; 错误! 未找到引用源。 野生水葫芦在第 1 到第 3 个月之间蔓延的平均速度等在第 2 到第 4 个月 之间蔓延的平均速度. 其中正确的说法有 . (请把正确说法的序号都 填在横线上)
2 2 2

8. 已 知 集 合 M ? { x | x ? 3 m ? 1 , m? Z } , N ? { y | y? 3n? 2 , n , ? Z }若 x0 ? M , y0 ? N , 1

17. ( Ⅰ )
f ( x) ? x ? 3 ?

1 7?x

1 1 3 ?2 (2 ) 2 ? (?9.6)0 ? (3 ) 3 ? (1.5) ?2 4 8









价 2 元,直到 16 周末,该服装已不再销售。 (Ⅰ)试建立价格 P 与周次 t 之间的函数关系式。 (Ⅱ)若此服装每件进价 Q 与周次 t 之间的关系为 Q ? ?0.125(t ? 8)
2

5 0 log ? 1 ?3 2 ? ? ? ?(? 2 ) ? 8 ? ?

1

2 + log2 3 ? log3 4

? 12 , t ??0,16? ,

t ? N ? ,试问该服装第几周每件销售利润最大?最大值是多少?

18.已知函数的定义域为集合

A,

(注:每件销售利润=售价-进价)

B ? ?x ? Z 2 ? x ? 10?, C ? ?x ? R x ? a或x ? a ? 1?
(1)求

A , (CR A) ? B ;

(2)若 A ? C ? R ,求实数 a 的取值范围。

19.已知函数 f ( x) ? x ?

a ? 2, x ? ?1,?? ? 。 x

21.对于定义域为 D 的函数 y ? f ( x) ,若同时满足下列条件:① f ( x) 在 D 内单调递增或单调递 减;②存在区间 [ a , b ] ? ( x ? D )叫闭函数。 (Ⅰ)求闭函数

(Ⅰ)当 a ?

1 时,利用函数单调性的定义判断并证明 f ( x) 的单调性,并求其值域; 2

D ,使 f ( x) 在 [ a , b ] 上的值域为 [ a , b ] ;那么把 y ? f ( x)

(Ⅱ)若对任意 x ?

?1,???, f ( x) ? 0 ,求实数 a 的取值范围。

y ? ? x 3 符合条件②的区间[ a , b ];
4 x

(Ⅱ)判断函数 f ( x) ? 3 x ? 1 ( x ? 0) 是否为闭函数?并说明理由; (Ⅲ)判断函数

y ? k ? x ? 2 是否为闭函数?若是闭函数,求实数 k 的取值范围。

20.季节性服装当季节即将来临时, 价格呈上升趋势, 设某服装开始时定价为 10 元, 并且每周 (7 天)涨价 2 元,5 周后开始保持 20 元的价格平稳销售;10 周后当季节即将过去时,平均每周削 2

3


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