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7. What comedians have in common with the players in a

   comedy is their way of playing with words.

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6. Acting our stereotypes of people from different countries

  can be very funny.

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5. Much of the wisdom discovered by early Chinese

  scientists is still useful for farming.

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4. Not only is food production important but also taking

   care of the environment.

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3. To make as much use of the land as possible, two or

  more crops are planted each year where possible.

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2. It is on this arable land that the farmers produce food

  for the whole population of China.

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1. What do you think causes these changes?

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12.(16分)已知函数f(x)=x2-4ax+2a+6(a∈R).

(1)若函数的值域为[0,+∞),求a的值;

(2)若函数值为非负数,求函数f(a)=2-a|a+3|的值域.

[解析] (1)∵函数的值域为[0,+∞),

∴Δ=16a2-4(2a+6)=0,

即2a2-a-3=0,得a=-1或a=.

(2)∵对一切x∈R函数值均为非负,

∴Δ=8(2a2-a-3)≤0⇒-1≤a≤,

∴a+3>0,

∴f(a)=2-a|a+3|

=-a2-3a+2

=-2+,

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11.(15分)已知函数f(x)=-xm,且f(4)=-.

(1)求m的值;

(2)判断f(x)在(0,+∞)上的单调性,并给予证明.

[解析] (1)f(4)=-,∴-4m=-,m=1.

(2)f(x)=-x在(0,+∞)上单调递减.

现证之:任取x1、x2∈(0,+∞)且x1<x2,则x2-x1>0,

∴f(x2)-f(x1)=-

=(x1-x2).

∵x2-x1>0,x1x2>0,∴f(x2)-f(x1)<0.

∴f(x)=-x,在(0,+∞)上单调递减.

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10.(15分)已知函数y=-x2+ax-+在区间[0,1)上的最大值是2,求实数a的值.

[解析] y=-2+(a2-a+2),对称轴为x=.

(1)当0≤≤1即0≤a≤2时,ymax=(a2-a+2),由(a2-a+2)=2得a=3或a=-2,与0≤a≤2矛盾,不合要求.

(2)当<0即a<0时,y在[0,1]上单调减,有ymax=f(0),由f(0)=2⇒-+=2⇒a=-6.

(3)当>1即a>2时,y在[0,1]上单调增,有ymax=f(1),由f(1)=2⇒-1+a-+=2⇒a=

综上,得a=-6或a=.

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