1.令2x+π/3=kπ,則x=(3k-1)π/6.對(duì)稱中心的坐標(biāo)是((3k-1)π/6,0) k是整數(shù).
令2x+π/3=(2k + 1/2)π或（2k - 1/2)π,則x=(12k+1)π/12或（12k-5)π/12.
對(duì)稱軸的方程是((12k+1)π/12,1)或（（12k-5)π/12,-1）k是整數(shù).
2.由f(1-x)=f(x+1)可知f(x)以x=1為對(duì)稱軸,
由f(x+1)=f(x-3)可得f(x)=f(x+4),即f(x)以4為周期.
x∈Io=[-1,1],f(x)=x,由上易得x∈[1,3]時(shí),f(x)=-x+2.
[-1,3]的區(qū)間長(zhǎng)度為4,恰與函數(shù)周期相等.在其他[-1+4k,3+4k](k為整數(shù)）中,函數(shù)圖像即可通過[-1,3]上的圖像進(jìn)行平移.經(jīng)分析可得,
當(dāng)x∈[-1+4k,1+4k],f(x)=x-4k
當(dāng)x∈[1+4k,3+4k],f(x)=-x+2+4k.
k為整數(shù).