对于f(x-2)＝f(x)和f(x+2)=f(x)的周期与对称轴的公式，怎么着自变量相同时两个小括 f（x＋2）＝－f（x）怎么求函数周期？
f(x)=f(2-x)\u7684\u5468\u671f\u662f\u591a\u5c11\uff1f\u5bf9\u79f0\u8f74\u600e\u4e48\u6c42\uff1f\u9996\u5148\uff0c\u5982\u679c\u53ea\u6709f(x)=f(2-x)\u8fd9\u4e2a\u5173\u7cfb\u7684\u8bdd\u662f\u6ca1\u6709\u5468\u671f\u7684\u3002
\u6211\u8ddf\u4f60\u8bf4\uff0c\u4e24\u51fd\u6570\u503c\u4f1a\u76f8\u7b49\uff0c\u4e00\u822c\u6709\u4e24\u79cd\u60c5\u51b5\uff0c\u4e00\u662f\u56e0\u4e3a\u5bf9\u79f0\u76f8\u7b49\uff0c\u4e8c\u662f\u56e0\u4e3a\u5468\u671f\u800c\u76f8\u7b49\u3002
\u800c\u51fa\u73b0f(x)=f(2-x)\u8fd9\u6837\u7684\u5f0f\u5b50\u4e2d\uff0c\u4f60\u5c31\u8981\u770b\u91cc\u9762\u7684\u53d8\u91cf\u7684\u7b26\u53f7\u662f\u5426\u76f8\u540c\uff0c\u82e5\u76f8\u540c\uff0c\u90a3\u4e48\u5e94\u5c5e\u4e8e\u5468\u671f\u51fd\u6570\u7684\u60c5\u51b5\uff0c\u82e5\u76f8\u53cd\uff0c\u5c31\u5c5e\u4e8e\u5bf9\u79f0\u8f74\u7684\u60c5\u51b5\u3002
\u56e0\u4e3a\u6211\u4eec\u8981\u6c42\u5bf9\u79f0\u8f74\u65f6\uff0c\u6839\u636e\u5bf9\u79f0\u6027\uff0c\u53ef\u4ee5\u9009\u4e24\u70b9\uff08\u8fd9\u4e24\u70b9\u7684\u51fd\u6570\u503c\u76f8\u7b49\uff09\u6765\u53d6\u4e2d\u70b9
\u90a3\u4e48\u7531f(x)=f(2-x)\u5c31\u53ef\u4ee5\u77e5\u9053\u5bf9\u79f0\u8f74\u662fx=[x+(2-x)]/2=1(\u7b26\u53f7\u76f8\u53cd\u5c31\u53ef\u4ee5\u7ea6\u6389\u561b)
\u5982\u679c\u51fa\u73b0\u7b26\u53f7\u76f8\u540c\u7684\u60c5\u51b5\uff0c\u5982f(x)=f(x+b)
\u663e\u7136\u4e00\u4e2a\u5468\u671f\u662fT=b
\u82e5\u662ff(x+a)=f(x+b)
\u90a3\u4e48\u5b83\u7684\u4e00\u4e2a\u6700\u5c0f\u6b63\u5468\u671f\u53ef\u4ee5\u8fd9\u6837\u6c42\uff1a
T=|(x+b)-(x+a)|=|b-a|(\u7b26\u53f7\u76f8\u540c\u76f8\u51cf\u5c31\u53ef\u4ee5\u7ea6\u6389)
\u5982\u679c\u4e0d\u61c2\uff0c\u8bf7Hi\u6211\uff0c\u795d\u5b66\u4e60\u6109\u5feb\uff01
\u7ed3\u679c\u4e3a\uff1a\u6b64\u51fd\u6570\u5468\u671f\u4e3a4
\u89e3\u9898\u8fc7\u7a0b\u5982\u4e0b\uff1a
f(x+2)=-f(x)
\u89e3\uff1a
=f(x+4)
=f(x+2+2)
=-f(x+2)
=-[-f(x)]
=f(x)
\u2234 f(x)\u7684\u5468\u671f\u662f4
\u6269\u5c55\u8d44\u6599\u6c42\u51fd\u6570\u5468\u671f\u7684\u65b9\u6cd5\uff1a
\u5bf9\u4e8e\u51fd\u6570y=f\uff08x\uff09\uff0c\u5982\u679c\u5b58\u5728\u4e00\u4e2a\u4e0d\u4e3a\u96f6\u7684\u5e38\u6570T\uff0c\u4f7f\u5f97\u5f53x\u53d6\u5b9a\u4e49\u57df\u5185\u7684\u6bcf\u4e00\u4e2a\u503c\u65f6\uff0cf\uff08x+T\uff09=f\uff08x\uff09\u90fd\u6210\u7acb\uff0c\u90a3\u4e48\u5c31\u628a\u51fd\u6570y=f\uff08x\uff09\u53eb\u505a\u5468\u671f\u51fd\u6570\uff0c\u4e0d\u4e3a\u96f6\u7684\u5e38\u6570T\u53eb\u505a\u8fd9\u4e2a\u51fd\u6570\u7684\u5468\u671f\u3002\u4e8b\u5b9e\u4e0a\uff0c\u4efb\u4f55\u4e00\u4e2a\u5e38\u6570kT\uff08k\u2208Z\uff0c\u4e14k\u22600\uff09\u90fd\u662f\u5b83\u7684\u5468\u671f\u3002
\u5e76\u4e14\u5468\u671f\u51fd\u6570f\uff08x\uff09\u7684\u5468\u671fT\u662f\u4e0ex\u65e0\u5173\u7684\u975e\u96f6\u5e38\u6570\uff0c\u4e14\u5468\u671f\u51fd\u6570\u4e0d\u4e00\u5b9a\u6709\u6700\u5c0f\u6b63\u5468\u671f\u3002
\u8bbef\uff08x\uff09\u662f\u5b9a\u4e49\u5728\u6570\u96c6M\u4e0a\u7684\u51fd\u6570\uff0c\u5982\u679c\u5b58\u5728\u975e\u96f6\u5e38\u6570T\u5177\u6709\u6027\u8d28\uff1af\uff08x+T\uff09=f\uff08x\uff09\uff0c\u5219\u79f0f\uff08x\uff09\u662f\u6570\u96c6M\u4e0a\u7684\u5468\u671f\u51fd\u6570\uff0c\u5e38\u6570T\u79f0\u4e3af\uff08x\uff09\u7684\u4e00\u4e2a\u5468\u671f\u3002\u5982\u679c\u5728\u6240\u6709\u6b63\u5468\u671f\u4e2d\u6709\u4e00\u4e2a\u6700\u5c0f\u7684\uff0c\u5219\u79f0\u5b83\u662f\u51fd\u6570f\uff08x\uff09\u7684\u6700\u5c0f\u6b63\u5468\u671f\u3002
\u7531\u5b9a\u4e49\u53ef\u5f97\uff1a\u5468\u671f\u51fd\u6570f\uff08x\uff09\u7684\u5468\u671fT\u662f\u4e0ex\u65e0\u5173\u7684\u975e\u96f6\u5e38\u6570\uff0c\u4e14\u5468\u671f\u51fd\u6570\u4e0d\u4e00\u5b9a\u6709\u6700\u5c0f\u6b63\u5468\u671f\uff0c\u8b6c\u5982\u72c4\u5229\u514b\u96f7\u51fd\u6570\u3002
\u5468\u671f\u51fd\u6570\u7684\u6027\u8d28\uff1a
\uff081\uff09\u82e5T\uff08\u22600\uff09\u662ff\uff08x\uff09\u7684\u5468\u671f\uff0c\u5219-T\u4e5f\u662ff\uff08x\uff09\u7684\u5468\u671f\u3002
\uff082\uff09\u82e5T\uff08\u22600\uff09\u662ff\uff08x\uff09\u7684\u5468\u671f\uff0c\u5219nT\uff08n\u4e3a\u4efb\u610f\u975e\u96f6\u6574\u6570\uff09\u4e5f\u662ff\uff08x\uff09\u7684\u5468\u671f\u3002
\uff083\uff09\u82e5T1\u4e0eT2\u90fd\u662ff\uff08x\uff09\u7684\u5468\u671f\uff0c\u5219T1\u00b1T2\u4e5f\u662ff\uff08x\uff09\u7684\u5468\u671f\u3002
\uff084\uff09\u82e5f\uff08x\uff09\u6709\u6700\u5c0f\u6b63\u5468\u671fT*\uff0c\u90a3\u4e48f\uff08x\uff09\u7684\u4efb\u4f55\u6b63\u5468\u671fT\u4e00\u5b9a\u662fT*\u7684\u6b63\u6574\u6570\u500d\u3002
\uff085\uff09\u82e5T1\u3001T2\u662ff\uff08x\uff09\u7684\u4e24\u4e2a\u5468\u671f\uff0c\u4e14T1/T2\u662f\u65e0\u7406\u6570\uff0c\u5219f\uff08x\uff09\u4e0d\u5b58\u5728\u6700\u5c0f\u6b63\u5468\u671f\u3002
\uff086\uff09\u5468\u671f\u51fd\u6570f\uff08x\uff09\u7684\u5b9a\u4e49\u57dfM\u5fc5\u5b9a\u662f\u81f3\u5c11\u4e00\u65b9\u65e0\u754c\u7684\u96c6\u5408\u3002
f(x-2)=f(x);f(x+2）=f(x).
联立求解：f(x+2)=f(x-2)
令x-2=t;
得到f(t)=f(t+4),所以周期T=4;
2.有关对称的结论：
f(x)=f(-x),关于x=0对称。
f(x)=f(2a-x),关于x=a对称。
f(x)=-f(-x),关于(0,0)对称。
f(x)=2b-f(-x),关于(0,b)对称。
f(x)=2b-f(2a-x),关于(a,b)对称。
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