有正比例,反比例,一次,二次,指数,对数,三角,幂函数。还有什么函数?上述这些函数有什么区别?

\u54ea\u4f4d\u5927\u795e\u5e2e\u5fd9\uff0c\u5341\u4e00\u4e2a\u51fd\u6570\u7684\u516b\u4e2a\u6027\u8d28\u6c42\u603b\u7ed3\uff08\u5927\u6982\u662f\u6b63\u6bd4\u4f8b\uff0c\u53cd\u6bd4\u4f8b\uff0c\u4e00\u6b21\uff0c\u4e8c\u6b21\uff0c\u5e42\u51fd\u6570\uff0c\u6307\u6570\uff0c\u5bf9\u6570\uff0c\u5bf9

\u8fd9\u662f\u521d\u4e2d\u9ad8\u4e2d\u6570\u5b66\u6240\u6709\u51fd\u6570\u7684\u6027\u8d28 \u56fe\u50cf
1.\u4e00\u6b21\u51fd\u6570(\u5305\u62ec\u6b63\u6bd4\u4f8b\u51fd\u6570) \u6700\u7b80\u5355\u6700\u5e38\u89c1\u7684\u51fd\u6570\uff0c\u5728\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb\u4e0a\u7684\u56fe\u8c61\u4e3a\u76f4\u7ebf\u3002
\u5b9a\u4e49\u57df\uff08\u4e0b\u9762\u6ca1\u6709\u8bf4\u660e\u7684\u8bdd\uff0c\u90fd\u662f\u5728\u65e0\u7279\u6b8a\u8981\u6c42\u60c5\u51b5\u4e0b\u7684\u5b9a\u4e49\u57df\uff09\uff1aR
\u503c\u57df\uff1aR
\u5947\u5076\u6027\uff1a\u65e0
\u5468\u671f\u6027\uff1a\u65e0
\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb\u89e3\u6790\u5f0f(\u4e0b\u7b80\u79f0\u89e3\u6790\u5f0f):
\u2460ax+by+c=0[\u4e00\u822c\u5f0f]
\u2461y=kx+b[\u659c\u622a\u5f0f]
\uff08k\u4e3a\u76f4\u7ebf\u659c\u7387\uff0cb\u4e3a\u76f4\u7ebf\u7eb5\u622a\u8ddd\uff0c\u6b63\u6bd4\u4f8b\u51fd\u6570b=0\uff09
\u2462y-y1=k(x-x1)[\u70b9\u659c\u5f0f]
\uff08k\u4e3a\u76f4\u7ebf\u659c\u7387,(x1,y1)\u4e3a\u8be5\u76f4\u7ebf\u6240\u8fc7\u7684\u4e00\u4e2a\u70b9\uff09
\u2463\uff08y-y1\uff09/(y2-y1)=(x-x1)/(x2-x1)[\u4e24\u70b9\u5f0f]
\uff08\uff08x1,y1\uff09\u4e0e\uff08x2,y2\uff09\u4e3a\u76f4\u7ebf\u4e0a\u7684\u4e24\u70b9\uff09
\u2464x/a-y/b=0[\u622a\u8ddd\u5f0f]
\uff08a\u3001b\u5206\u522b\u4e3a\u76f4\u7ebf\u5728x\u3001y\u8f74\u4e0a\u7684\u622a\u8ddd\uff09
\u89e3\u6790\u5f0f\u8868\u8fbe\u5c40\u9650\u6027\uff1a
\u2460\u6240\u9700\u6761\u4ef6\u8f83\u591a\uff083\u4e2a\uff09\uff1b
\u2461\u3001\u2462\u4e0d\u80fd\u8868\u8fbe\u6ca1\u6709\u659c\u7387\u7684\u76f4\u7ebf\uff08\u5e73\u884c\u4e8ex\u8f74\u7684\u76f4\u7ebf\uff09\uff1b
\u2463\u53c2\u6570\u8f83\u591a\uff0c\u8ba1\u7b97\u8fc7\u4e8e\u70e6\u7410\uff1b
\u2464\u4e0d\u80fd\u8868\u8fbe\u5e73\u884c\u4e8e\u5750\u6807\u8f74\u7684\u76f4\u7ebf\u548c\u8fc7\u5706\u70b9\u7684\u76f4\u7ebf\u3002
\u503e\u659c\u89d2\uff1ax\u8f74\u5230\u76f4\u7ebf\u7684\u89d2\uff08\u76f4\u7ebf\u4e0ex\u8f74\u6b63\u65b9\u5411\u6240\u6210\u7684\u89d2\uff09\u79f0\u4e3a\u76f4\u7ebf\u7684\u503e\u659c \u89d2\u3002\u8bbe\u4e00\u76f4\u7ebf\u7684\u503e\u659c\u89d2\u4e3aa\uff0c\u5219\u8be5\u76f4\u7ebf\u7684\u659c\u7387k=tg(a)\u3002

2.\u4e8c\u6b21\u51fd\u6570
\u9898\u76ee\u4e2d\u5e38\u89c1\u7684\u51fd\u6570\uff0c\u5728\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb\u4e0a\u7684\u56fe\u8c61\u662f\u4e00\u6761\u5bf9\u79f0\u8f74\u4e0ey\u8f74\u5e73\u884c\u7684\u629b\u7269\u7ebf\u3002
\u5b9a\u4e49\u57df\uff1aR
\u503c\u57df\uff1a\uff08\u5bf9\u5e94\u89e3\u6790\u5f0f\uff0c\u4e14\u53ea\u8ba8\u8bbaa\u5927\u4e8e0\u7684\u60c5\u51b5\uff0ca\u5c0f\u4e8e0\u7684\u60c5\u51b5\u8bf7\u8bfb\u8005\u81ea\u884c\u63a8\u65ad\uff09\u2460[(4ac-b^2)/4a\uff0c\u6b63\u65e0\u7a77\uff09\uff1b\u2461[t\uff0c\u6b63\u65e0\u7a77\uff09
\u5947\u5076\u6027\uff1a\u5076\u51fd\u6570
\u5468\u671f\u6027\uff1a\u65e0
\u89e3\u6790\u5f0f\uff1a
\u2460y=ax^2+bx+c[\u4e00\u822c\u5f0f]
\u2474a\u22600
\u2475a\uff1e0\uff0c\u5219\u629b\u7269\u7ebf\u5f00\u53e3\u671d\u4e0a\uff1ba\uff1c0\uff0c\u5219\u629b\u7269\u7ebf\u5f00\u53e3\u671d\u4e0b\uff1b
\u2476\u6781\u503c\u70b9\uff1a\uff08-b/2a\uff0c(4ac-b^2)/4a\uff09\uff1b
\u2477\u0394=b^2-4ac,
\u0394\uff1e0\uff0c\u56fe\u8c61\u4e0ex\u8f74\u4ea4\u4e8e\u4e24\u70b9\uff1a
\uff08[-b+\u221a\u0394]/2a\uff0c0\uff09\u548c\uff08[-b+\u221a\u0394]/2a\uff0c0\uff09\uff1b
\u0394\uff1d0\uff0c\u56fe\u8c61\u4e0ex\u8f74\u4ea4\u4e8e\u4e00\u70b9\uff1a
\uff08-b/2a\uff0c0\uff09\uff1b
\u0394\uff1c0\uff0c\u56fe\u8c61\u4e0ex\u8f74\u65e0\u4ea4\u70b9\uff1b
\u2461y=a(x-h)^2+t[\u914d\u65b9\u5f0f]
\u6b64\u65f6\uff0c\u5bf9\u5e94\u6781\u503c\u70b9\u4e3a\uff08h\uff0ct\uff09\uff0c\u5176\u4e2dh=-b/2a\uff0ct=(4ac-b^2)/4a\uff09\uff1b

3.\u53cd\u6bd4\u4f8b\u51fd\u6570
\u5728\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb\u4e0a\u7684\u56fe\u8c61\u4e3a\u53cc\u66f2\u7ebf\u3002
\u5b9a\u4e49\u57df\uff1a\uff08\u8d1f\u65e0\u7a77\uff0c0\uff09\u222a\uff080\uff0c\u6b63\u65e0\u7a77\uff09
\u503c\u57df\uff1a\uff08\u8d1f\u65e0\u7a77\uff0c0\uff09\u222a\uff080\uff0c\u6b63\u65e0\u7a77\uff09
\u5947\u5076\u6027\uff1a\u5947\u51fd\u6570
\u5468\u671f\u6027\uff1a\u65e0
\u89e3\u6790\u5f0f\uff1ay=1/x

4.\u5e42\u51fd\u6570
y=x^a
\u2460y=x^3
\u5b9a\u4e49\u57df\uff1aR
\u503c\u57df\uff1aR
\u5947\u5076\u6027\uff1a\u5947\u51fd\u6570
\u5468\u671f\u6027\uff1a\u65e0
\u56fe\u8c61\u7c7b\u4f3c\u4e8e\u5c06\u4e00\u4e2a\u8fc7\u5706\u70b9\u7684\u4e8c\u6b21\u51fd\u6570\u7684\u7b2c\u56db\u533a\u95f4\u90e8\u5206\u5173\u4e8ex\u8f74\u4f5c\u8f74\u5bf9\u79f0
\u540e\u5f97\u5230\u7684\u56fe\u8c61\uff08\u7c7b\u6bd4\uff0c\u8fd9\u4e2a\u65b9\u6cd5\u4e0d\u80fd\u5f97\u5230\u4e09\u6b21\u51fd\u6570\u56fe\u8c61\uff09
\u2461y=x^(1/2)
\u5b9a\u4e49\u57df\uff1a[0\uff0c\u6b63\u65e0\u7a77\uff09
\u503c\u57df\uff1a[0\uff0c\u6b63\u65e0\u7a77\uff09
\u5947\u5076\u6027\uff1a\u65e0\uff08\u5373\u975e\u5947\u975e\u5076\uff09
\u5468\u671f\u6027\uff1a\u65e0
\u56fe\u8c61\u7c7b\u4f3c\u4e8e\u5c06\u4e00\u4e2a\u8fc7\u5706\u70b9\u7684\u4e8c\u6b21\u51fd\u6570\u4ee5\u539f\u70b9\u4e3a\u65cb\u8f6c\u4e2d\u5fc3\uff0c\u987a\u65f6\u9488\u65cb\u8f6c
90\u00b0\uff0c\u518d\u53bb\u6389y\u8f74\u4e0b\u65b9\u90e8\u5206\u5f97\u5230\u7684\u56fe\u8c61\uff08\u7c7b\u6bd4\uff0c\u8fd9\u4e2a\u65b9\u6cd5\u4e0d\u80fd\u5f97\u5230\u4e09\u6b21
\u51fd\u6570\u56fe\u8c61\uff09

5.\u6307\u6570\u51fd\u6570
\u5728\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb\u4e0a\u7684\u56fe\u8c61\uff08\u592a\u96be\u63cf\u8ff0\u4e86\uff0c\u8bf4\u4e00\u4e0b\u6027\u8d28\u5427\u2026\u2026\uff09
\u6052\u8fc7\u70b9\uff080\uff0c1\uff09\u3002\u8054\u7cfb\u89e3\u6790\u5f0f\uff0c\u82e5a\uff1e1\u5219\u51fd\u6570\u5728\u5b9a\u4e49\u57df\u4e0a\u5355\u8c03\u589e\uff1b\u82e50\uff1ca\uff1c1 \u5219\u51fd\u6570\u5728\u5b9a\u4e49\u57df\u4e0a\u5355\u8c03\u51cf\u3002
\u5b9a\u4e49\u57df\uff1aR
\u503c\u57df\uff1a\uff080\uff0c\u6b63\u65e0\u7a77\uff09
\u5947\u5076\u6027\uff1a\u65e0
\u5468\u671f\u6027\uff1a\u65e0
\u89e3\u6790\u5f0f\uff1ay=a^x
a\uff1e0
\u6027\u8d28\uff1a\u4e0e\u5bf9\u6570\u51fd\u6570y=log(a)x\u4e92\u4e3a\u53cd\u51fd\u6570\u3002
*\u5bf9\u6570\u8868\u8fbe\uff1alog(a)x\u8868\u793a\u4ee5a\u4e3a\u5e95\u7684x\u7684\u5bf9\u6570\u3002

6.\u5bf9\u6570\u51fd\u6570
\u5728\u5b9a\u4e49\u57df\u4e0a\u7684\u56fe\u8c61\u4e0e\u5bf9\u5e94\u7684\u6307\u6570\u51fd\u6570\uff08\u8be5\u5bf9\u6570\u51fd\u6570\u7684\u53cd\u51fd\u6570\uff09\u7684\u56fe\u8c61\u5173\u4e8e\u76f4\u7ebfy=x\u8f74\u5bf9\u79f0\u3002
\u6052\u8fc7\u5b9a\u70b9\uff081\uff0c0\uff09\u3002\u8054\u7cfb\u89e3\u6790\u5f0f\uff0c\u82e5a\uff1e1\u5219\u51fd\u6570\u5728\u5b9a\u4e49\u57df\u4e0a\u5355\u8c03\u589e\uff1b\u82e50\uff1ca\uff1c1 \u5219\u51fd\u6570\u5728\u5b9a\u4e49\u57df\u4e0a\u5355\u8c03\u51cf\u3002
\u5b9a\u4e49\u57df\uff1a\uff080\uff0c\u6b63\u65e0\u7a77\uff09
\u503c\u57df\uff1aR
\u5947\u5076\u6027\uff1a\u65e0
\u5468\u671f\u6027\uff1a\u65e0
\u89e3\u6790\u5f0f\uff1ay=log(a)x
a\uff1e0
\u6027\u8d28\uff1a\u4e0e\u5bf9\u6570\u51fd\u6570y=a^x\u4e92\u4e3a\u53cd\u51fd\u6570\u3002

7.\u4e09\u89d2\u51fd\u6570
\u2474\u6b63\u5f26\u51fd\u6570\uff1ay=sinx
\u56fe\u8c61\u4e3a\u6b63\u5f26\u66f2\u7ebf\uff08\u4e00\u79cd\u6ce2\u6d6a\u7ebf\uff0c\u662f\u6240\u6709\u66f2\u7ebf\u7684\u57fa\u7840\uff09
\u5b9a\u4e49\u57df\uff1aR
\u503c\u57df\uff1a[-1\uff0c1]
\u5947\u5076\u6027\uff1a\u5947\u51fd\u6570
\u5468\u671f\u6027\uff1a\u6700\u5c0f\u6b63\u5468\u671f\u4e3a2\u03c0
\u5bf9\u79f0\u8f74\uff1a\u76f4\u7ebfx=k\u03c0/2 (k\u2208Z\uff09
\u4e2d\u5fc3\u5bf9\u79f0\u70b9\uff1a\u4e0ex\u8f74\u7684\u4ea4\u70b9\uff1a\uff08k\u03c0\uff0c0\uff09(k\u2208Z\uff09

\u2475\u4f59\u5f26\u51fd\u6570\uff1ay=cosx
\u56fe\u8c61\u4e3a\u6b63\u5f26\u66f2\u7ebf\uff0c\u7531\u6b63\u5f26\u51fd\u6570\u7684\u56fe\u8c61\u5411\u5de6\u5e73\u79fb\u03c0/2\u4e2a\u5355\u4f4d\uff08\u6700\u5c0f\u5e73\u79fb\u91cf\uff09\u6240\u5f97\u3002
\u5b9a\u4e49\u57df\uff1aR
\u503c\u57df\uff1a[-1\uff0c1]
\u5947\u5076\u6027\uff1a\u5076\u51fd\u6570
\u5468\u671f\u6027\uff1a\u6700\u5c0f\u6b63\u5468\u671f\u4e3a2\u03c0
\u5bf9\u79f0\u8f74\uff1a\u76f4\u7ebfx=k\u03c0 (k\u2208Z\uff09
\u4e2d\u5fc3\u5bf9\u79f0\u70b9\uff1a\u4e0ex\u8f74\u7684\u4ea4\u70b9\uff1a\uff08\u03c0/2+k\u03c0\uff0c0\uff09(k\u2208Z\uff09

\u2476\u6b63\u5207\u51fd\u6570\uff1ay=tg x
\u56fe\u8c61\u7684\u6bcf\u4e2a\u5468\u671f\u5355\u4f4d\u5f88\u50cf\u662f\u4e09\u6b21\u51fd\u6570\uff0c\u5f88\u591a\u4e2a\uff0c\u5747\u5300\u5206\u5e03\u5728x\u8f74\u4e0a\u3002
\u5b9a\u4e49\u57df\uff1a{x\u2502x\u2260\u03c0/2+k\u03c0}
\u503c\u57df\uff1aR
\u5947\u5076\u6027\uff1a\u5947\u51fd\u6570
\u5468\u671f\u6027\uff1a\u6700\u5c0f\u6b63\u5468\u671f\u4e3a\u03c0
\u5bf9\u79f0\u8f74\uff1a\u65e0
\u4e2d\u5fc3\u5bf9\u79f0\u70b9\uff1a\u4e0ex\u8f74\u7684\u4ea4\u70b9\uff1a\uff08k\u03c0\uff0c0\uff09(k\u2208Z\uff09\u3002

*\u4e09\u89d2\u51fd\u6570\u7684\u6027\u8d28\u7565\u4e86\uff0c\u592a\u591a\uff0c\u5149\u516c\u5f0f\u5c31\u4e0d\u6b62\u5343\u4e2a\u3002\u53e6\u5916\uff0c\u4e09\u89d2\u51fd\u6570\u7684\u56fe\u8c61\u5e73\u79fb\u3001\u62c9\u4f38\u53d8\u5316\uff0c\u5728\u56fe\u8c61\u5e73\u79fb\u5185\u5bb9\u4e2d\u8bf4\u5f97\u5f88\u6e05\u695a\uff08\u4e0d\u5728\u8fd9\u91cc\uff0c\u5728\u6559\u6750\u91cc\uff09\u6211\u5c31\u4e0d\u591a\u8bf4\u4e86\u3002

\u6b63\u6bd4\u4f8b\u51fd\u6570,\u53cd\u6bd4\u4f8b\u51fd\u6570,\u4e00\u6b21\u51fd\u6570,\u4e8c\u6b21\u51fd\u6570,\u6307\u6570\u51fd\u6570,\u5bf9\u6570\u51fd\u6570,\u5e42\u51fd\u6570\u3001\u516d\u79cd\u4e09\u89d2\u51fd\u6570,\u53cd\u4e09\u89d2\u51fd\u6570

正比例函数就是关于原点对称的直线,反比例函数是跟原点相对的两个抛物线,一次函数是直线,二次是抛物线,指数函数可以转化为对数函数,它们是相对的,三角函数就是根据三角形的三边算出sin . cos. sec. tan. cot 的值,幂函数就是开方

  • 涓娆鍑芥暟,姝f瘮渚鍑芥暟,浜屾鍑芥暟,鍙嶆瘮渚鍑芥暟鐨勬ц川?
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