函数y=f（x）是什么意思，f（x）不是代表了y吗？y=2x+3可以写成f（x）=2x+3吗？
\u9ad8\u4e2d\u51fd\u6570y=f(x)\u4e2d\u7684f\u5230\u5e95\u662f\u4ec0\u4e48\u610f\u601d\uff1f\uff01 \u4e3a\u4ec0\u4e48\u4f1a\u51fa\u73b0f(3)=___\u8fd9\u79cd\u9898\u76ee\uff1f\uff01 f(2x-f(x)\u5176\u5b9e\u8ddf\u6211\u4eec\u4e4b\u524d\u5b66\u7684y=kx+b\u4e00\u6837 \u6709\u4e2a\u901a\u5f0f f(2x-3)\u7684\u610f\u601d\u5c31\u662f\u628a2x-3\u4ee3\u5230\u5f0f\u5b50\u91cc\u9762\u53bb\u6c42\u503c \u4e5f\u5c31\u662f\u6c42y\u4e86
\u5728\u6570\u5b66\u9886\u57df\uff0c\u51fd\u6570\u662f\u4e00\u79cd\u5173\u7cfb\uff0c\u8fd9\u79cd\u5173\u7cfb\u4f7f\u4e00\u4e2a\u96c6\u5408\u91cc\u7684\u6bcf\u4e00\u4e2a\u5143\u7d20\u5bf9\u5e94\u5230\u53e6\u4e00\u4e2a\uff08\u53ef\u80fd\u76f8\u540c\u7684\uff09\u96c6\u5408\u91cc\u7684\u552f\u4e00\u5143\u7d20\u3002 \u81ea\u53d8\u91cf\uff0c\u51fd\u6570\u4e00\u4e2a\u4e0e\u4ed6\u91cf\u6709\u5173\u8054\u7684\u53d8\u91cf\uff0c\u8fd9\u4e00\u91cf\u4e2d\u7684\u4efb\u4f55\u4e00\u503c\u90fd\u80fd\u5728\u4ed6\u91cf\u4e2d\u627e\u5230\u5bf9\u5e94\u7684\u56fa\u5b9a\u503c\u3002 \u51fd\u6570\u4e24\u7ec4\u5143\u7d20\u4e00\u4e00\u5bf9\u5e94\u7684\u89c4\u5219\uff0c\u7b2c\u4e00\u7ec4\u4e2d\u7684\u6bcf\u4e2a\u5143\u7d20\u5728\u7b2c\u4e8c\u7ec4\u4e2d\u53ea\u6709\u552f\u4e00\u7684\u5bf9\u5e94\u91cf\u3002 \u51fd\u6570\u7684\u6982\u5ff5\u5bf9\u4e8e\u6570\u5b66\u548c\u6570\u91cf\u5b66\u7684\u6bcf\u4e00\u4e2a\u5206\u652f\u6765\u8bf4\u90fd\u662f\u6700\u57fa\u7840\u7684\u3002 \uff5e\u2016\u51fd\u6570\u7684\u5b9a\u4e49\uff1a \u8bbex\u548cy\u662f\u4e24\u4e2a\u53d8\u91cf\uff0cD\u662f\u5b9e\u6570\u96c6\u7684\u67d0\u4e2a\u5b50\u96c6\uff0c\u82e5\u5bf9\u4e8eD\u4e2d\u7684\u6bcf\u4e2a\u503cx\uff0c\u53d8\u91cfy\u6309\u7167\u4e00\u5b9a\u7684\u6cd5\u5219\u6709\u4e00\u4e2a\u786e\u5b9a\u7684\u503cy\u4e0e\u4e4b\u5bf9\u5e94\uff0c\u79f0\u53d8\u91cfy\u4e3a\u53d8\u91cfx\u7684\u51fd\u6570\uff0c\u8bb0\u4f5c y=f(x). \u6570\u96c6D\u79f0\u4e3a\u51fd\u6570\u7684\u5b9a\u4e49\u57df\uff0c\u7531\u51fd\u6570\u5bf9\u5e94\u6cd5\u5219\u6216\u5b9e\u9645\u95ee\u9898\u7684\u8981\u6c42\u6765\u786e\u5b9a\u3002\u76f8\u5e94\u7684\u51fd\u6570\u503c\u7684\u5168\u4f53\u79f0\u4e3a\u51fd\u6570\u7684\u503c\u57df\uff0c\u5bf9\u5e94\u6cd5\u5219\u548c\u5b9a\u4e49\u57df\u662f\u51fd\u6570\u7684\u4e24\u4e2a\u8981\u7d20\u3002 functions \u6570\u5b66\u4e2d\u7684\u4e00\u79cd\u5bf9\u5e94\u5173\u7cfb\uff0c\u662f\u4ece\u975e\u7a7a\u96c6\u5408A\u5230\u5b9e\u6570\u96c6B\u7684\u5bf9\u5e94\u3002\u7b80\u5355\u5730\u8bf4\uff0c\u7532\u968f\u7740\u4e59\u53d8\uff0c\u7532\u5c31\u662f\u4e59\u7684\u51fd\u6570 \u3002\u7cbe\u786e\u5730\u8bf4\uff0c\u8bbeX\u662f\u4e00\u4e2a\u975e\u7a7a\u96c6\u5408\uff0cY\u662f\u975e\u7a7a\u6570\u96c6 \uff0cf\u662f\u4e2a\u5bf9\u5e94\u6cd5\u5219 \uff0c \u82e5\u5bf9X\u4e2d\u7684\u6bcf\u4e2ax\uff0c\u6309\u5bf9\u5e94\u6cd5\u5219f\uff0c\u4f7fY\u4e2d\u5b58\u5728\u552f\u4e00\u7684\u4e00\u4e2a\u5143\u7d20y\u4e0e\u4e4b\u5bf9\u5e94 \uff0c \u5c31\u79f0\u5bf9\u5e94\u6cd5\u5219f\u662fX\u4e0a\u7684\u4e00\u4e2a\u51fd\u6570\uff0c\u8bb0\u4f5cy\uff1df\uff08x\uff09\uff0c\u79f0X\u4e3a\u51fd\u6570f\uff08x\uff09\u7684\u5b9a\u4e49\u57df\uff0c\u96c6\u5408{y|y=f\uff08x\uff09\uff0cx\u2208R}\u4e3a\u5176\u503c\u57df\uff08\u503c\u57df\u662fY\u7684\u5b50\u96c6\uff09\uff0cx\u53eb\u505a\u81ea\u53d8\u91cf\uff0cy\u53eb\u505a\u56e0\u53d8\u91cf\uff0c\u4e60\u60ef\u4e0a\u4e5f\u8bf4y\u662fx\u7684\u51fd\u6570\u3002 \u82e5\u5148\u5b9a\u4e49\u6620\u5c04\u7684\u6982\u5ff5\uff0c\u53ef\u4ee5\u7b80\u5355\u5b9a\u4e49\u51fd\u6570\u4e3a\uff1a\u5b9a\u4e49\u5728\u975e\u7a7a\u6570\u96c6\u4e4b\u95f4\u7684\u6620\u5c04\u79f0\u4e3a\u51fd\u6570\u3002 \u4f8b1\uff1ay\uff1dsinx X\uff1d\uff3b0\uff0c2\u03c0\uff3d\uff0cY\uff1d\uff3b\uff0d1\uff0c1\uff3d \uff0c\u5b83\u7ed9\u51fa\u4e86\u4e00\u4e2a\u51fd\u6570\u5173\u7cfb\u3002\u5f53\u7136 \uff0c\u628aY\u6539\u4e3aY1\uff1d\uff08a\uff0cb\uff09 \uff0ca\uff1cb\u4e3a\u4efb\u610f\u5b9e\u6570\uff0c\u4ecd\u7136\u662f\u4e00\u4e2a\u51fd\u6570\u5173\u7cfb\u3002 \u5176\u6df1\u5ea6y\u4e0e\u4e00\u5cb8\u8fb9\u70b9 O\u5230\u6d4b\u91cf\u70b9\u7684\u8ddd\u79bb x \u4e4b\u95f4\u7684\u5bf9\u5e94\u5173\u7cfb\u5448\u66f2\u7ebf\uff0c\u8fd9\u4ee3\u8868\u4e00\u4e2a\u51fd\u6570\uff0c\u5b9a\u4e49\u57df\u4e3a\uff3b0\uff0cb\uff3d\u3002\u4ee5\u4e0a3\u4f8b\u5c55\u793a\u4e86\u51fd\u6570\u7684\u4e09\u79cd\u8868\u793a\u6cd5\uff1a\u516c\u5f0f\u6cd5 \uff0c \u8868\u683c\u6cd5\u548c\u56fe \u50cf\u6cd5\u3002 \u4e00\u822c\u5730\uff0c\u5728\u4e00\u4e2a\u53d8\u5316\u8fc7\u7a0b\u4e2d\uff0c\u5982\u679c\u6709\u4e24\u4e2a\u53d8\u91cfX\u4e0eY\uff0c\u5e76\u4e14\u5bf9\u4e8eX\u7684\u6bcf\u4e00\u4e2a\u786e\u5b9a\u7684\u503c\uff0cY\u90fd\u6709\u4e3a\u4e00\u5f97\u503c\u4e0e\u5176\u5bf9\u5e94\uff0c\u90a3\u4e48\u6211\u4eec\u5c31\u8bf4X\u662f\u81ea\u53d8\u91cf\uff0cY\u662fX\u7684\u51fd\u6570\u3002\u5982\u679c\u5f53X=A\u65f6Y=B\uff0c\u90a3\u4e48B\u53eb\u505a\u5f53\u81ea\u53d8\u91cf\u7684\u503c\u4e3aA\u65f6\u7684\u51fd\u6570\u503c\u3002 \u590d\u5408\u51fd\u6570 \u67093\u4e2a\u53d8\u91cf\uff0cy\u662fu\u7684\u51fd\u6570\uff0cy\uff1d\u03c8\uff08u\uff09\uff0cu\u662fx\u7684\u51fd\u6570\uff0cu\uff1df\uff08x\uff09\uff0c\u5f80\u5f80\u80fd\u5f62\u6210\u94fe\uff1ay\u901a\u8fc7\u4e2d\u95f4\u53d8\u91cfu\u6784\u6210\u4e86x\u7684\u51fd\u6570\uff1a x\u2192u\u2192y\uff0c\u8fd9\u8981\u770b\u5b9a\u4e49\u57df\uff1a\u8bbe\u03c8\u7684\u5b9a\u4e49\u57df\u4e3aU \u3002 f\u7684\u503c\u57df\u4e3aU\uff0c\u5f53U*ÍU\u65f6\uff0c\u79f0f\u4e0e\u03c8 \u6784\u6210\u4e00\u4e2a\u590d\u5408\u51fd\u6570 \uff0c \u4f8b\u5982 y\uff1dlgsinx\uff0cx\u2208\uff080\uff0c\u03c0\uff09\u3002\u6b64\u65f6sinx\uff1e0 \uff0clgsinx\u6709\u610f\u4e49 \u3002\u4f46\u5982\u82e5\u89c4\u5b9ax\u2208\uff08\uff0d\u03c0\uff0c0\uff09\uff0c\u6b64\u65f6sinx\uff1c0 \uff0clgsinx\u65e0\u610f\u4e49 \uff0c\u5c31\u6210\u4e0d\u4e86\u590d\u5408\u51fd\u6570\u3002
y=f（x）的意思是：y是关于x的函数简单情况下，两者一致，可以互相替换。
复杂情况下，一般用需要f(x)而不是y来表示函数关系,y更多的是用来表示纵坐标。
复杂情况是指：
1、函数有多个自变量，此时可能y本身就是自变量，比如f(x,y)=5x+3y
2、同一个自变量，可能有多个函数关系。比如对于x
f(x)=5x+2
g(x)=3x²-27
答1函数y=f（x）的意思
是y是关于x的函数
2f（x）整体是代表了y，
且f（x）有具体的表达式
3y=2x+3可以写成f（x）=2x+3
也可以写成y=f（x）=2x+3
也可以写成y=g（x）=2x+3
f(x)代表的是2x+3这个函数表达式，y代表的是因变量！
绛旓細灏辨槸璇碮鏄叧浜庤嚜鍙橀噺X鐨勪竴涓嚱鏁般侳锛圶锛夊氨鏄寚浠涓鸿嚜鍙橀噺鐨鍑芥暟锛孎(X)鏄搴斿彉閲忋傛瘮濡侳锛圶锛=2X 锛y=f(x)锛岄偅Y=2X锛屼袱涓槸涓涓鎰忔銆
绛旓細y=f(x)琛ㄧずy鍏充簬x鐨鍑芥暟銆倅鏄鍑芥暟鐨勫簲鍙橀噺锛=琛ㄧず绠楁湳鐩哥瓑锛岃〃绀虹敱璇ュ嚱鏁板畾涔夊煙鍒拌鍑芥暟鍊煎煙鐨勫搴旀硶鍒欎笖璇ユ硶鍒欏搴旂殑鏄犲皠蹇呴』鏄崟灏勶紝锛堬級鍐呯殑鏄鍑芥暟鐨勫簲鍙橀噺銆傚y=f锛坸锛=2x+3灏辨槸琛ㄧず涓涓嚱鏁 鍊煎緱娉ㄦ剰鐨勬槸锛屽鏋滀竴涓嚱鏁版湁鍙嶅嚱鏁板瓨鍦紝鍒欒鍑芥暟瀵瑰簲鐨勬槧灏勬棦鍗曚笖婊°備篃灏辨槸璇磋鍑芥暟鍦...
绛旓細杩欓噷 X Y閮戒唬琛ㄦ湭鐭ユ暟 鑰f()浠ｈ〃鐨勬槸閫氳繃涓瀹氱殑璁＄畻杩囩▼ 鏁翠釜鎰忔灏辨槸Y鏄閫氳繃X缁忚繃涓瀹氱殑璁＄畻杩囩▼寰楁潵鐨 f锛欰鈫払 杩欎釜F鍚屾牱鎸囪绠楄繃绋 A B灏卞ソ姣斿垰鎵嶈鐨刋 Y 閮芥槸鏈煡鏁 閫氳繃绠ご 鍙互鐞嗚В涓 浠鐨勮绠楁柟寮 鐢辨湭鐭ユ暟A璁＄畻鎴愪负鏈煡鏁癇 ...
绛旓細鏁伴泦D绉颁负杩欎釜鍑芥暟鐨勫畾涔夊煙銆2銆乫锛欰鈫払涓紝鍊煎煙鏄泦鍚圔鐨勫瓙闆嗐傚锛歠(x)=x,閭ｄ箞f(x)鐨勫彇鍊艰寖鍥村氨鏄鍑芥暟f(x)鐨勫煎煙銆3銆佷竴鑸湴璇达紝鍦ㄥ嚱鏁拌鍙y = f(x)涓紝鈥渇鈥濆嵆琛ㄧず瀵瑰簲娉曞垯锛岀瓑寮弝 = f(x)琛ㄦ槑锛屽浜庡畾涔夊煙涓殑浠绘剰鐨剎鍊硷紝鍦ㄥ搴旀硶鍒欌渇鈥濈殑浣滅敤涓嬶紝鍗冲彲寰楀埌鍊煎煙涓敮涓y鍊笺
绛旓細姣斿绗竴涓鍑芥暟 f(x)=6x+7 锛岀浜屼釜鍑芥暟 g(x)=7x-4銆俧(4) = 6*4+7銆俫(5) = 7*5-4銆傚嚱鏁扮殑瀹氫箟锛氱粰瀹氫竴涓暟闆咥锛屽亣璁惧叾涓殑鍏冪礌涓簒銆傜幇瀵笰涓殑鍏冪礌x鏂藉姞瀵瑰簲娉曞垯f锛璁颁綔f锛坸锛夛紝寰楀埌鍙︿竴鏁伴泦B銆傚亣璁綛涓殑鍏冪礌涓簓銆傚垯y涓巟涔嬮棿鐨勭瓑閲忓叧绯诲彲浠ョ敤y=f锛坸锛琛ㄧず銆傚嚱鏁版蹇靛惈鏈変笁...
绛旓細鑰宖灏辨槸娌熼氳嚜鍙橀噺鍜屽洜鍙橀噺鐨勬ˉ姊.涓句緥:y=x^2-2x+3.杩欓噷濡備綍灏唜鍜寉瀵瑰簲璧锋潵鍛(f鐨勫惈涔)?灏辨槸灏嗚嚜鍙橀噺(x)鐨勫钩鏂瑰噺鍘昏嚜鍙橀噺鐨2鍊嶅啀鍔3,灏卞緱鍒板洜鍙橀噺.鑷充簬浣犺鐨2f,3f,4f,鎴戞病鐞嗚В浠涔堟剰鎬.浣犲彲浠ュ皢f(x)灏辩湅鎴愬洜鍙橀噺.2f(x),3f(x)琛ㄧず2鍊嶇殑f(x),3鍊嶇殑f(x).鑰宖(x)鐨勫钩鏂瑰彲浠ュ啓鎴...
绛旓細x)鐨勮嚜鍙橀噺鏄痻锛岃寉鐨勮嚜鍙橀噺鍗翠笉鐭ラ亾锛屽洜涓哄彲鑳芥槸y=k 1锛岄偅鑷彉閲忓氨鏄痥浜嗐傛墍浠ョ敤f(x)鏇磋兘琛ㄨ揪鍑鸿嚜鍙橀噺鍜屽洜鍙橀噺鐨勫叧绯汇f(x)鏄楂樹竴鏁板涓殑鐭ヨ瘑鐐癸紝閫氬父缁欏畾涓涓潪绌虹殑鏁伴泦A,瀵笰鏂藉姞瀵瑰簲娉曞垯f,璁颁綔f锛圓锛,寰楀埌鍙︿竴鏁伴泦B,涔熷氨鏄疊=f锛A锛.閭ｄ箞杩欎釜鍏崇郴寮忓氨鍙鍑芥暟鍏崇郴寮忋
绛旓細瑙ｆ瀽锛//绮楃暐瑙ｉ噴// 涓鑸潵璇达紝鍑芥暟浼氬啓浣y=f(x)姝ゅ锛宖鏄搴旀硶鍒欙紝(x)琛ㄧず浠モ滄嫭鍙蜂腑鐨勫唴瀹逛綔涓鸿嚜鍙橀噺鈥濄備綘鍙兘浼氶棶锛屼负浠涔堣瀛︽垚杩欐牱鍛紵鍘熷洜鏈変簩锛(1) 鏁板鐨勭壒鐐瑰氨鏄細绗﹀彿鍖栵紝绠娲佸寲銆備笘鐣岄氱敤闃挎媺浼暟瀛楋紝涓嶅氨鏄洜涓鸿繖涓師鍥犲悧锛(2) f鏄function(鍑芥暟)鐨勯瀛楁瘝 锝烇綖锝為殣鍑芥暟 涓句緥璇...
绛旓細鏄嚜鍙橀噺x鏄犲皠鍒板洜鍙橀噺y鐨勨滃搴旀硶鍒欌濓紝渚嬪y=f(x)=x^2锛宖鐨勬剰涔夊氨鏄嚜鍙橀噺鐨勫钩鏂广傚悓鏃舵敞鎰忥紝涓涓鍑芥暟鐨刦鏄浐瀹氱殑锛屼緥濡倅=f(x)=x^2锛屽垯y=f(t)=t^2锛屽搴旀硶鍒欎笉鍙楄嚜鍙橀噺鐨勮〃绀烘柟娉曠殑褰卞搷銆傚笇鏈涙垜鐨勫洖绛斿彲浠ュ府鍒颁綘銆
绛旓細f锛坸锛夋槸涓涓互x涓鸿嚜鍙橀噺鐨勫嚱鏁般傚綋鍑芥暟y=f锛坸锛鐨勮嚜鍙橀噺x鍦ㄤ竴鐐箈0涓婁骇鐢熶竴涓閲徫攛鏃讹紝鍑芥暟杈撳嚭鍊肩殑澧為噺螖y涓庤嚜鍙橀噺澧為噺螖x鐨勬瘮鍊煎湪螖x瓒嬩簬0鏃剁殑鏋侀檺a濡傛灉瀛樺湪锛宎鍗充负鍦▁0澶勭殑瀵兼暟锛岃浣渇'锛坸0锛夋垨df锛坸0锛/dx銆傚鏋滃嚱鏁皔=f锛坸锛夊湪寮鍖洪棿鍐呮瘡涓鐐归兘鍙锛屽氨绉鍑芥暟f锛坸锛夊湪鍖洪棿鍐...
