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问题 解答题

设a为实数，函数f（x）=x|x-a|，其中x∈R．

（1）分别写出当a=0．a=2．a=-2时函数f（x）的单调区间；

（2）判断函数f（x）的奇偶性，并加以证明．

答案

（1）当a=0时，f（x）=x|x|=

x2    x≥0
-x2  x＜0
，

f（x）的单调递增区间为（-∞，+∞）；（2分）

当a=2时，f(x)=

x2-2xx≥2
-x2+2xx＜2
f（x）的单调递增区间为（-∞，1）和（2，+∞）；f（x）的单调递减区间为（1，2）

当a=-2时，f(x)=

x2+2xx≥-2
-x2-2xx＜-2
f（x）的单调递增区间为（-∞，-2）和（-1，+∞）；f（x）的单调递减区间为（-2，-1）

（2）当a=0时，f（x）=x|x|，所以f（x）为奇函数

因为定义域为R关于原点对称，且f（-x）=-x|-x|=-f（x）

所以f（x）为奇函数

当a≠0时，f（x）=x|x-a|为非奇非偶函数，

f（a）=0，f（-a）=-a|2a|，所以f（-a）≠f（a），f（-a）≠-f（a）

所以f（x）是非奇非偶函数．

单项选择题

引起言语失用的病灶部位位于（）

A.颈内动脉和大脑中动脉分布区

B.优势侧颞枕顶叶结合区

C.优势侧颞上回后1/3区域及其周围部位

D.大脑左半球前部语言中枢Broca区附近

E.优势侧额下回后部皮质或皮质下
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填空题

Of all the employed workers in the United States, 12.5 million are part of a temporary workforce. The United States Bureau of Labor Statistics counts 9.2 percent of workers as those who have______(1) they term "alternative employment arrangements." The government predicts that temporary staffing agencies______(2) experience growth of 49 percent by 2010. If numbers increase at the rate ______ (3), these companies will add 1.9 million new jobs by 2010. That’’s more than any______(4) industry.Temporary workers were the first ones to be affected by the recent economic recession, but they are______(5) to be the first to regain positions as the economy picks up and companies work to rebuild. Employers use temporary workers as a resource because_______(6) offer flexibility and come at a low cost. Many temporaries are categorized as "independent contractors" instead of employees,______(7) allows the employer to avoid______(8) certain taxes. Because they are not required to offer benefits to temporary workers, companies can save a great deal of money by hiring temps. Usually, temporary workers can qualify_______(9) benefits if they work for a staffing company for a certain length of time. Most temps, however, do not continue with one company long______(10) to qualify for them because they regard the position as a step on the ladder to a______(11) position later.According to Richard Wahlquist, president of the American Staffing Association, 75_______(12) of temporary workers hope for transition out of the temporary staffing category______(13) a period of time. Wahlquist finds that temporary workers spend about 11 weeks on various assignments before their______(14) out of the temporary workforce. Many use temporary positions to gain experience and skills______(15) they move on to better jobs. Wahlquist says that the temp workforce as a whole turns______(16) 400 percent each year.Tom Dilworth, research director at the Employment Policies Institute, explains______(17) some workers like having temporary jobs______(18) it affords them a great deal of elasticity with time and everything. Some temps only have a limited______(19) of time to work and temp agencies can help coordinate jobs to fit their schedules. Other sometimes-employees use temporary jobs to get an______(20) to a company from the inside, to get a foot in the door of a certain business or career._______(21) others take temporary positions in hopes their employers will change them over to permanent positions eventually.Nearly all the industries in the United States use temporary workers.______(22) to Tim Costello, coordinator of the North American Alliance for Fair Employment, the growth of temporary labor threatens______(23) job security of permanent workers who fear replacement, as well as the temps who are more accustomed to turnover. He predicts that there will continue to______(24) a gradual shift from permanent employees to contingent staffing, and that such a_____(25) in workplace demographics will "lead to lower wages, poorer working conditions, and more instability."
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