已知f(x)是偶函数，x ÎR，若将f(x)的图象向右平移一个单位又得到一个奇函
数，又f(2)＝－1，则f(1)+ f(2)+ f(3)+…+ f(2011)＝ （ ）
A．－1003
B．1003
C．1
D．－1
答案：D
解：∵将f（x）的图象向右平移一个单位得到一个奇函数，
即f（x-1）是奇函数，∴f（-x-1）=-f（x-1），
又f（x）是偶函数，∴f（-x-1）=f（x+1），
∴f（x+1））=-f（x-1），
∴f（（x-1）+4）=-f（（x-1）+2）=f（x-1），可得f（x+4）=f（x），
∴函数f（x）的周期为4，
∵平移前f（x）是偶函数，f（x-1）是奇函数，x∈R，∴f（-1）=f（1）=f（3）=0，
f（0）=-f（-2）=-f（2）=1，
∴f（1）+f（2）+f（3）+…+f（2006）=501（f（1）+f（2）+f（3）+f（4））+f（1）+f（2）=-1，
故选D．
Shaking It Off  One day, a farmer’s donkey fell into a dry well(井). The poor animal cried for hours before his finally found him. The farmer tried hard to pull him out from the well but failed. He felt for the donkey but after carefully thinking about the situation, he that he would save neither the donkey nor the well. Since the donkey was too and it was not worth（值得） the trouble of saving. So he invited his neighbors to help him bury(埋葬) the old donkey in the __ so that it would make him end his pain. many people coming to help, the old donkey was excited at first. As they began to scoop the dirt into the well with shovels(铲子), he soon what was happening. He felt upset and cried sadly again. As the farmer and his neighbors continued throwing the dirt on his , he suddenly had a good idea. Some time later, when the farmer finally looked down into the well, he was surprised at what he saw: the dirt landed on his back, he would shake it off and take a step up! Soon, everyone was amazed when the donkey stepped over the edge of the well and ran away quickly! It seemed that it would him at first, but it actually helped him later because of the manner in which he faced his adversity(逆境). That is life! Just like the donkey, life is going to throw dirt on us, all kinds of dirt. we face our problems in an active way, and refuse to to any trouble, each dirt is like a stepping stone with which we get out of the deepest wells. This is a key one of the secrets of life. stop and never give up. Success is just in its way.
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