为什么f（x+2）是偶函数，那么f（x）的对称轴为x=2？ f(x+2)为偶函数，为什么f(-x+2)=f(x+2)而不...
f\uff08x+2\uff09\u662f\u5076\u51fd\u6570\uff0c\u5219\u5b83\u7684\u5bf9\u79f0\u8f74\u662f\u591a\u5c11\uff0c\u662fx=f(x+2)\u7684\u5bf9\u79f0\u8f74\u5c31\u662fx=0
f(x)\u7684\u5bf9\u79f0\u8f74\u662fx=2.\u56e0\u4e3af(x)\u76f8\u5f53\u4e8ef(x+2)\u5411\u53f3\u5e73\u79fb2\u4e2a\u5355\u4f4d\uff08\u5de6\u52a0\u53f3\u51cf\uff09
\u51fd\u6570\u662f\u5173\u4e8ex\u7684\uff0c\u53c8\u4e0d\u662f\u5173\u4e8e2\u7684\u3002\u8bf4f(x+2)\u662f\u5076\u51fd\u6570\uff0c\u662f\u9488\u5bf9x\u8bf4\u7684\uff0c\u5c31\u662f\u8bf4\u4e0d\u7ba1\u662fx\u8fd8\u662f-x\uff0c\u5176\u51fd\u6570\u503c\u76f8\u7b49\u3002
\u5982\u679c\u51fd\u6570f\uff08x\uff09\u7684\u5b9a\u4e49\u57df\u5173\u4e8e\u539f\u70b9\u5bf9\u79f0\uff0c\u4e14\u5b9a\u4e49\u57df\u5185\u4efb\u610f\u4e00\u4e2ax\uff0c\u90fd\u6709f\uff08-x\uff09=f\uff08x\uff09\uff0c\u90a3\u4e48\u51fd\u6570f\uff08x\uff09\u5c31\u53eb\u505a\u5076\u51fd\u6570\uff0c\u5176\u56fe\u8c61\u7279\u70b9\u662f\u5173\u4e8ey\u8f74\u5bf9\u79f0\u3002\u5b9a\u4e49\u57df\u5173\u4e8e\u539f\u70b9\u5bf9\u79f0\u3002
\u5076\u51fd\u6570\u7684\u6027\u8d28\uff1a
1\u3001\u5076\u51fd\u6570\u56fe\u8c61\u5173\u4e8ey\u8f74\u5bf9\u79f0\uff0c\u53cd\u4e4b\u4ea6\u7136\uff1b
2\u3001\u5076\u51fd\u6570\u5728\u5173\u4e8e\u539f\u70b9\u5bf9\u79f0\u7684\u4e24\u4e2a\u533a\u95f4\u4e0a\uff0c\u5355\u8c03\u6027\u76f8\u53cd\u3002
\u6269\u5c55\u8d44\u6599
\u5076\u51fd\u6570\u7684\u548c\u3001\u5dee\u3001\u79ef\u3001\u5546(\u5206\u6bcd\u4e0d\u4e3a\u96f6)\u4ecd\u4e3a\u5076\u51fd\u6570\u3002
\u4e00\u4e2a\u5947\u51fd\u6570\u4e0e\u4e00\u4e2a\u5076\u51fd\u6570\u7684\u79ef\u4e3a\u5947\u51fd\u6570\u3002
\u5947\u51fd\u6570+\u5076\u51fd\u6570=\u975e\u5947\u975e\u5076\u51fd\u6570\u3002
\u5224\u65ad\u51fd\u6570\u7684\u5947\u5076\u6027\uff0c\u5305\u62ec\u4e24\u4e2a\u5fc5\u5907\u6761\u4ef6\uff1a
\u4e00\u662f\u5b9a\u4e49\u57df\u5173\u4e8e\u539f\u70b9\u5bf9\u79f0\uff0c\u8fd9\u662f\u51fd\u6570\u5177\u6709\u5947\u5076\u6027\u7684\u5fc5\u8981\u4e0d\u5145\u5206\u6761\u4ef6\uff0c\u6240\u4ee5\u5148\u8003\u8651\u5b9a\u4e49\u57df\u662f\u89e3\u51b3\u95ee\u9898\u7684\u524d\u63d0\uff0c\u5982\u679c\u4e00\u4e2a\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u5173\u4e8e\u5750\u6807\u539f\u70b9\u4e0d\u5bf9\u79f0\u3002\u90a3\u4e48\u8fd9\u4e2a\u51fd\u6570\u5c31\u5931\u53bb\u4e86\u662f\u5947\u51fd\u6570\u6216\u662f\u5076\u51fd\u6570\u7684\u6761\u4ef6\u3002
\u4e8c\u662f\u5224\u65adf(x)\u4e0ef(-x)\u662f\u5426\u5177\u6709\u7b49\u91cf\u5173\u7cfb\u5728\u5224\u65ad\u5947\u5076\u6027\u7684\u8fd0\u7b97\u4e2d\uff0c\u53ef\u4ee5\u8f6c\u5316\u4e3a\u5224\u65ad\u5947\u5076\u6027\u7684\u7b49\u4ef7\u7b49\u91cf\u5173\u7cfb\u5f0f(f(x)+f(-x)=0(\u5947\u51fd\u6570)\u6216f(x)-f(-x)=0(\u5076\u51fd\u6570))\u662f\u5426\u6210\u7acb\u3002
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绛旓細2銆佷粈涔堟槸濂囧嚱鏁般3銆佸嚱鏁版湁濂囧伓鎬х殑鍓嶆彁銆4銆浠涔堟槸鍋跺嚱鏁銆1.濂囧嚱鏁帮細濡傛灉瀵逛簬鍑芥暟f(x)鐨勫畾涔夊煙鍐呬换鎰忎竴涓獂锛岄兘鏈塮(-x)=-f(x)锛閭ｄ箞鍑芥暟f(x)灏卞彨鍋氬鍑芥暟銆2.鍋跺嚱鏁帮細濡傛灉瀵逛簬鍑芥暟f(x)鐨勫畾涔夊煙鍐呬换鎰忎竴涓獂锛岄兘鏈塮(-x)=f(x)锛岄偅涔堝嚱鏁癴(x)灏卞彨鍋氬伓鍑芥暟銆3.鐗瑰埆鍦帮細濡傛灉瀵逛簬鍑芥暟...
绛旓細鍛婅瘔浣犱竴涓緢濂界殑璇绐嶏紝鍋氳繖绉嶉鐩槸涓瀹氳鐢诲浘锛岀敾鍥惧悗寰堢畝鍗曚篃鍙互鐢ㄦ潵妫楠 鎴戝厛璇寸浜岄锛岃繖鏍锋湁鍒╀簬浣犵悊瑙ｇ涓棰 鈥涓轰粈涔鏈夌殑鏃跺檉(x+2)=f(-x-2),鏈夌殑鏃跺檉(x+2)=f(-x+2),鍒板簳鍝釜瀵癸紵鈥濋偅浣犺鐪嬮鐩粰鐨勯偅涓槸鍋跺嚱鏁帮紝f(x)杩樻槸f(x+2)锛屽鏋f(x)鏄伓鍑芥暟锛閭ｄ箞f(x)=f(-...
绛旓細y=sin x^2 f锛-x锛=sin(-x)^2=f(x)鎵浠鏄伓鍑芥暟 D锛屼护g锛坸锛=y=f锛坸锛-f锛-x锛 g锛-x锛=f锛-x锛-f锛坸锛夋槸濂囧嚱鏁 鎵浠ラ塀锛岀瓟妗堥敊璇
绛旓細涓涓嚱鏁版棦鏄鍑芥暟鍙鏄伓鍑芥暟鏃讹紝鎰忓懗鐫璇ュ嚱鏁版弧瓒充互涓嬩袱涓ц川锛1. 濂囧嚱鏁扮殑鎬ц川锛氬浜庝换鎰忓疄鏁 x锛屾湁 f(-x) = -f(x)銆傚嵆鍑芥暟鍏充簬鍘熺偣瀵圭О锛屽绉拌酱鏄 y 杞淬2. 鍋跺嚱鏁扮殑鎬ц川锛氬浜庝换鎰忓疄鏁 x锛屾湁 f(-x) = f(x)銆傚嵆鍑芥暟鍏充簬 y 杞村绉般備竴涓嚱鏁板悓鏃舵弧瓒冲鍑芥暟鍜屽伓鍑芥暟鐨勬ц川锛屽繀椤...
绛旓細杩欎釜闂纭疄鏄緢闅剧殑.[[1]]鐢卞伓鍑芥暟瀹氫箟鍙煡,鑻ュ嚱鏁癵(x)鏄伓鍑芥暟,鍒欐亽鏈 g(-x)=g(x).[[2]]搴旇鏄庣櫧,鍑芥暟f(x+2)鏄鍚堝嚱鏁.鍗:y=f(u)u=x+2.棰樼洰鐨勬剰鎬濇槸,鍏充簬x鐨勫嚱鏁癴(x+2)鏄伓鍑芥暟.灏辨槸,杩欎釜鍑芥暟鏈缁堝彲鍖栦负x鐨勫嚱鏁,鍙涓篻(x)=f(x+2)鏁単(x)涓哄伓鍑芥暟.鈭磄(-x)=g...
绛旓細2銆佹弧瓒砯(-x) = - f(x)3銆佸叧浜庡師鐐瑰绉扮殑鍖洪棿涓婂崟璋冩т竴鑷 4銆佸鏋滃鍑芥暟鍦▁=0涓婃湁瀹氫箟,閭ｄ箞鏈塮(0)=0 5銆佸畾涔夊煙鍏充簬鍘熺偣瀵圭О锛堝鍋跺嚱鏁板叡鏈夌殑锛夊伓鍑芥暟鎬ц川锛1銆佸浘璞″叧浜巠杞村绉 2銆佹弧瓒砯(-x) = f(x)3銆佸叧浜庡師鐐瑰绉扮殑鍖洪棿涓婂崟璋冩х浉鍙 4銆佸鏋滀竴涓嚱鏁版棦鏄鍑芥暟鏈鏄伓鍑芥暟,閭ｄ箞鏈...
绛旓細2銆 涓涓伓鍑芥暟涓庝竴涓鍑芥暟鐩稿姞鎵寰楃殑鍜屾垨鐩稿噺鎵寰楃殑宸负闈炲闈炲伓鍑芥暟銆3銆佷袱涓鍑芥暟鐩镐箻鎵寰楃殑绉垨鐩搁櫎鎵寰楃殑鍟涓哄伓鍑芥暟銆4銆佷竴涓伓鍑芥暟涓庝竴涓鍑芥暟鐩镐箻鎵寰楃殑绉垨鐩搁櫎鎵寰楃殑鍟嗕负濂囧嚱鏁般5銆佸綋涓斾粎褰撳垎f锛坸锛=0锛堝畾涔夊煙鍏充簬鍘熺偣瀵圭О锛夋椂锛宖锛坸锛鏃㈡槸濂囧嚱鏁板張鏄伓鍑芥暟銆傚鍑芥暟鍦ㄥ绉...
绛旓細鍥犱负瀛樺湪甯告暟椤癸紝鍙互涓惧弽渚嬶細f'(x)=3*x^2鏄伓鍑芥暟锛鍘熷嚱鏁板鏋滄槸f(x)=x^3灏辨槸濂囧嚱鏁帮紝浣嗘槸鍘熷嚱鏁颁篃鍙兘鏄痜(x)=x^3+1锛岄偅灏变笉鏄鍑芥暟浜嗐傚鏁版槸鍑芥暟鐨勫眬閮ㄦц川銆備竴涓嚱鏁板湪鏌愪竴鐐圭殑瀵兼暟鎻忚堪浜嗚繖涓嚱鏁板湪杩欎竴鐐归檮杩戠殑鍙樺寲鐜囥傚鏋滃嚱鏁扮殑鑷彉閲忓拰鍙栧奸兘鏄疄鏁扮殑璇濓紝鍑芥暟鍦ㄦ煇涓鐐圭殑瀵兼暟灏辨槸...
绛旓細f(x+2)鏄伓鍑芥暟鐨勮瘽锛寈鍙栫浉鍙嶆暟鏃讹紝鍑芥暟鍊兼兂绛夛紝鍗虫瘮濡傝f锛-1+2锛=f(1+2),f锛2+2锛=f锛2+-2锛.銆傛墍浠ュ湪鍙0鏃讹紝x=2鏈夊敮涓鐨剏鍊间笌涔嬪搴旓紝鎵浠(x)鏈夊绉拌酱涓簒=2
绛旓細f(x+2) = f(-x-2) 鏄敊璇殑銆傛纭殑搴旇鏄 f(x+2) = f(-x+2) 銆傝姝ｇ‘鐞嗚В鍋跺嚱鏁扮殑瀹氫箟锛氭弧瓒 f(-x) = f(x) 鐨勫嚱鏁般傛湰棰樹腑锛寉 = f(x+2) 鏄伓鍑芥暟锛涓嶆槸 f(x) 鏄伓鍑芥暟銆傚彲浠ヤ护 g(x) = f(x+2) 锛寉 = g(x) 鏄伓鍑芥暟锛岄偅涔 g(-x) = g(x) 锛屽啓鍑烘潵灏...
