已知函数f（x）=|x|x-2ax+b（x∈R）．给出下列命题：
①f（x）可能是奇函数；
②f（x）可能是偶函数；
③当f（0）=f（2）时f（x）的图象必关于x=1对称；
④f（x）在（a，+∞）上是增函数
其中正确命题的序号是______．
①b=0时，函数是奇函数，可知①正确；
②当b≠0时，f（x）不具有奇偶性；故②错；
③令a=1，b=0，则f（x）=|x|x-2x
此时f（0）=f（2）=2，
但f（x）=|x|x-2x是奇函数，其图象不关于x=1对称；故③错；
④f（x）=|x|x-2ax+b=
，它的对称中心为（0．b），x2- 2ax+b，x≥0 -x2-2ax+b，x＜0
因此f（x）在（a，+∞）上单调递增，故④正确．
故答案为：①④．
| 完形填空 A loving person lives in a loving world.A hostile (敌意的) person lives in a hostile world.Everyone you meet is your mirror. Mirrors have a very particular__1__.They reflect the image in front of them.Just as a__2__mirror works as the vehicle to reflection, __3__do all of the people in our lives. When we see something beautiful such as a flower garden, that garden__4__a reflection.When we love someone, it's a(n)__5__of loving ourselves.We have often heard things like "I love how I am when I'm with that person". That simply__6__into "I'm able to love me when I love that other person". __7__, when we meet someone new, we feel as though we "click". Sometimes it's as if we've__8__each other for a long time.That feeling can come from__9__similarities. Just as the "mirror" or other people can be a positive reflection, it is more likely that we'll__10__it when it has a negative connotation (内涵). __11__, it's easy to remember the times when we have met someone we're not particularly__12__about.We may have some criticism (批评) in our mind about the__13__.This is especially true when we get to know someone with whom we would rather spend__14__time. Oftentimes, when we__15__qualities in other people, ironically (讽刺地), it's usually the mirror that's __16__to us. At times we meet someone__17__and feel distant, disconnected, or disgusted.__18__we don't want to believe it, and it's not easy or__19__to look further, it can be a great learning lesson to__20__what part of the person is being reflected in you.It's simply just another way to create more selfawareness. | ||||
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