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给出定义:若 m- 1 2 <x≤m+ 1 2 (m∈Z),则称m为离实数x最近的整数,记作{x}=m,在此基础上给出下列关于函数f(x)=|x-{x}|的五个命题: ①函数y=f(x)的定义域为R,值域为 [0, 1 2 ] ; ②函数y=f(x)是周期函数,最小正周期为1; ③函数y=f(x)在 [- 1 2 , 1 2 ] 上是增函数; ④函数y=f(x)的图象关于直线 x= k 2 (k∈Z)对称; ⑤函数y=f(x)的图象关于点(k,0)(k∈Z)对称. 其中正确的命题有( )个.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAgCAYAAABzenr0AAAA5ElEQVRYR2NkGGDAOMD2M+B0wKpVq9huv/jbxPD/fxwDA4MkhQ59zsDIuEhVgrkuLCzsF7JZOB3QOml5B8P//+UUWoyqnZGxszovsoI4B0xc9gyfzxmZmb2rcsK3IRvWMWm599///7fgcfTz6vwoKWId8B+f75kZGX0q8iK3kugAhur8KJRQxx0FE5fhdQC5UTPqgNEQGA2B0RAYDYHREBgNgaETAuTW96TqG7yt4tbRFhGRIQBqHTP9+8dIoDUMTxqk5AK8zXKYiaDWMYhNpANIaJYPdMdkwLtmpOZnctUPeDkAAP6tmiH1ggTLAAAAAElFTkSuQmCC)
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