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函数图：用相似三角形与平移展示函数关系的动态图解

函数图：用相似三角形与平移展示函数关系的动态图解
几何画板及绘图内容加载中，请稍等……
2018-09-19 02:13
测试改名0函数变换几何作图函数图像
① 本范例通过GeoGebra构建了一个名为“Function Diagrams”的动态图解，直观展示函数f在定义域与值域之间的对应关系，并利用相似三角形和几何变换（平移）来辅助理解函数映射。② 核心数学概念包括函数图像、相似三角形、几何变换（平移）、以及函数值的可视化表示，涉及点、线段、交点等基本几何元素。③ 作图要点：从构造摘要可见，使用了Intersect（求交点）、Point（点）、Line（直线）、Segment（线段）、Textfield（文本输入框）等命令，并定义了多个对象如width、f、start、A1~A25、B1~B7等，通过大量点与线段的组合构建出函数图的结构，可能包含可调节参数（如width）和动态文本输入。④ 适合中学数学阶段（如初中高年级或高中）学习函数概念、几何变换与相似三角形综合应用时使用，也可用于教师课堂演示或学生自主探索函数性质。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(yAxis) → B
  3. Line(A, B) → a
  4. Line(C, a) → b
  5. Segment(B1, C1) → D1
  6. Segment(B2, C2) → D2
  7. Segment(B3, C3) → D3
  8. Segment(B4, C4) → D4
  9. Segment(B5, C5) → D5
  10. Segment(B6, C6) → D6
  11. Segment(B7, C7) → D7
  12. Segment(B8, C8) → D8
  13. Segment(B9, C9) → D9
  14. Segment(B10, C10) → D10
  15. Segment(B11, C11) → D11
  16. Segment(B12, C12) → D12
  17. Segment(B13, C13) → D13
  18. Segment(B14, C14) → D14
  19. Segment(B15, C15) → D15
  20. Segment(B16, C16) → D16
  21. Segment(B17, C17) → D17
  22. Segment(B18, C18) → D18
  23. Segment(B19, C19) → D19
  24. Segment(B20, C20) → D20
  25. Segment(B21, C21) → D21
  26. Segment(B22, C22) → D22
  27. Segment(B23, C23) → D23
  28. Segment(B24, C24) → D24
  29. Segment(B25, C25) → D25
  30. Segment(B26, C26) → D26
  31. Segment(B27, C27) → D27
  32. Segment(B28, C28) → D28
  33. Segment(B29, C29) → D29
  34. Segment(B30, C30) → D30
  35. Segment(B31, C31) → D31
  36. Segment(B32, C32) → D32
  37. Segment(B33, C33) → D33
  38. Segment(B34, C34) → D34
  39. Segment(B35, C35) → D35
  40. Segment(B36, C36) → D36
  41. Segment(B37, C37) → D37
  42. Segment(B38, C38) → D38
  43. Segment(B39, C39) → D39
  44. Segment(B40, C40) → D40
  45. Segment(B41, C41) → D41
  46. Segment(B42, C42) → D42
  47. Segment(B43, C43) → D43
  48. Segment(B44, C44) → D44
  49. Segment(B45, C45) → D45
  50. Segment(B46, C46) → D46
  51. Segment(B47, C47) → D47
  52. Segment(B48, C48) → D48
  53. Segment(B49, C49) → D49
  54. Segment(B50, C50) → D50
  55. Segment(B51, C51) → D51
  56. Segment(B52, C52) → D52
  57. Segment(B53, C53) → D53
  58. Segment(B54, C54) → D54
  59. Segment(B55, C55) → D55
  60. Segment(B56, C56) → D56
  61. Segment(B57, C57) → D57
  62. Segment(B58, C58) → D58
  63. Segment(B59, C59) → D59
  64. Segment(B60, C60) → D60
  65. Segment(B61, C61) → D61
  66. Segment(B62, C62) → D62
  67. Segment(B63, C63) → D63
  68. Segment(B64, C64) → D64
  69. Segment(B65, C65) → D65
  70. Segment(B66, C66) → D66
  71. Segment(B67, C67) → D67
  72. Segment(B68, C68) → D68
  73. Segment(B69, C69) → D69
  74. Segment(B70, C70) → D70
  75. Segment(B71, C71) → D71
  76. Segment(B72, C72) → D72
  77. Segment(B73, C73) → D73
  78. Segment(B74, C74) → D74
  79. Segment(B75, C75) → D75
  80. Segment(B76, C76) → D76
  81. Segment(B77, C77) → D77
  82. Segment(B78, C78) → D78
  83. Segment(B79, C79) → D79
  84. Segment(B80, C80) → D80
  85. Segment(B81, C81) → D81
  86. Segment(B82, C82) → D82
  87. Segment(B83, C83) → D83
  88. Segment(B84, C84) → D84
  89. Segment(B85, C85) → D85
  90. Segment(B86, C86) → D86
  91. Segment(B87, C87) → D87
  92. Segment(B88, C88) → D88
  93. Segment(B89, C89) → D89
  94. Segment(B90, C90) → D90
  95. Segment(B91, C91) → D91
  96. Segment(B92, C92) → D92
  97. Segment(B93, C93) → D93
  98. Segment(B94, C94) → D94
  99. Segment(B95, C95) → D95
  100. Segment(B96, C96) → D96
  101. Segment(B97, C97) → D97
  102. Segment(B98, C98) → D98
  103. Segment(B99, C99) → D99
  104. Segment(B100, C100) → D100
  105. Segment(B101, C101) → D101
  106. Segment(B102, C102) → D102
  107. Segment(B103, C103) → D103
  108. Segment(B104, C104) → D104
  109. Segment(B105, C105) → D105
  110. Segment(B106, C106) → D106
  111. Segment(B107, C107) → D107
  112. Segment(B108, C108) → D108
  113. Segment(B109, C109) → D109
  114. Segment(B110, C110) → D110
  115. Segment(B111, C111) → D111
  116. Segment(B112, C112) → D112
  117. Segment(B113, C113) → D113
  118. Segment(B114, C114) → D114
  119. Segment(B115, C115) → D115
  120. Segment(B116, C116) → D116
  121. Segment(B117, C117) → D117
  122. Segment(B118, C118) → D118
  123. Segment(B119, C119) → D119
  124. Segment(B120, C120) → D120
  125. Segment(B121, C121) → D121
  126. Segment(B122, C122) → D122
  127. Segment(B123, C123) → D123
  128. Segment(B124, C124) → D124
  129. Segment(B125, C125) → D125
  130. Segment(B126, C126) → D126
  131. Segment(B127, C127) → D127
  132. Segment(B128, C128) → D128
  133. Segment(B129, C129) → D129
  134. Segment(B130, C130) → D130
  135. Segment(B131, C131) → D131
  136. Segment(B132, C132) → D132
  137. Segment(B133, C133) → D133
  138. Segment(B134, C134) → D134
  139. Segment(B135, C135) → D135
  140. Segment(B136, C136) → D136
  141. Segment(B137, C137) → D137
  142. Segment(B138, C138) → D138
  143. Segment(B139, C139) → D139
  144. Segment(B140, C140) → D140
  145. Segment(B141, C141) → D141
  146. Segment(B142, C142) → D142
  147. Segment(B143, C143) → D143
  148. Segment(B144, C144) → D144
  149. Segment(B145, C145) → D145
  150. Segment(B146, C146) → D146
  151. Segment(B147, C147) → D147
  152. Segment(B148, C148) → D148
  153. Segment(B149, C149) → D149
  154. Segment(B150, C150) → D150
  155. Segment(B151, C151) → D151
  156. Segment(B152, C152) → D152
  157. Segment(B153, C153) → D153
  158. Segment(B154, C154) → D154
  159. Segment(B155, C155) → D155
  160. Segment(B156, C156) → D156
  161. Segment(B157, C157) → D157
  162. Segment(B158, C158) → D158
  163. Segment(B159, C159) → D159
  164. Segment(B160, C160) → D160
  165. Segment(B161, C161) → D161
  166. Segment(B162, C162) → D162
  167. Segment(B163, C163) → D163
  168. Segment(B164, C164) → D164
  169. Segment(B165, C165) → D165
  170. Segment(B166, C166) → D166
  171. Segment(B167, C167) → D167
  172. Segment(B168, C168) → D168
  173. Segment(B169, C169) → D169
  174. Segment(B170, C170) → D170
  175. Segment(B171, C171) → D171
  176. Segment(B172, C172) → D172
  177. Segment(B173, C173) → D173
  178. Segment(B174, C174) → D174
  179. Segment(B175, C175) → D175
  180. Segment(B176, C176) → D176
  181. Segment(B177, C177) → D177
  182. Segment(B178, C178) → D178
  183. Segment(B179, C179) → D179
  184. Segment(B180, C180) → D180
  185. Segment(B181, C181) → D181
  186. Segment(B182, C182) → D182
  187. Segment(B183, C183) → D183
  188. Segment(B184, C184) → D184
  189. Segment(B185, C185) → D185
  190. Segment(B186, C186) → D186
  191. Segment(B187, C187) → D187
  192. Segment(B188, C188) → D188
  193. Segment(B189, C189) → D189
  194. Segment(B190, C190) → D190
  195. Segment(B191, C191) → D191
  196. Segment(B192, C192) → D192
  197. Segment(B193, C193) → D193
  198. Segment(B194, C194) → D194
  199. Segment(B195, C195) → D195
  200. Segment(B196, C196) → D196
  201. Segment(B197, C197) → D197
  202. Segment(B198, C198) → D198
  203. Segment(B199, C199) → D199
  204. Segment(B200, C200) → D200
  205. Segment(B1, F1) → G1
  206. Segment(B2, F2) → G2
  207. Segment(B3, F3) → G3
  208. Segment(B4, F4) → G4
  209. Segment(B5, F5) → G5
  210. Segment(B6, F6) → G6
  211. Segment(B7, F7) → G7
  212. Segment(B8, F8) → G8
  213. Segment(B9, F9) → G9
  214. Segment(B10, F10) → G10
  215. Segment(B11, F11) → G11
  216. Segment(B12, F12) → G12
  217. Segment(B13, F13) → G13
  218. Segment(B14, F14) → G14
  219. Segment(B15, F15) → G15
  220. Segment(B16, F16) → G16
  221. Segment(B17, F17) → G17
  222. Segment(B18, F18) → G18
  223. Segment(B19, F19) → G19
  224. Segment(B20, F20) → G20
  225. Segment(B21, F21) → G21
  226. Segment(B22, F22) → G22
  227. Segment(B23, F23) → G23
  228. Segment(B24, F24) → G24
  229. Segment(B25, F25) → G25
  230. Segment(B26, F26) → G26
  231. Segment(B27, F27) → G27
  232. Segment(B28, F28) → G28
  233. Segment(B29, F29) → G29
  234. Segment(B30, F30) → G30
  235. Segment(B31, F31) → G31
  236. Segment(B32, F32) → G32
  237. Segment(B33, F33) → G33
  238. Segment(B34, F34) → G34
  239. Segment(B35, F35) → G35
  240. Segment(B36, F36) → G36
  241. Segment(B37, F37) → G37
  242. Segment(B38, F38) → G38
  243. Segment(B39, F39) → G39
  244. Segment(B40, F40) → G40
  245. Segment(B41, F41) → G41
  246. Segment(B42, F42) → G42
  247. Segment(B43, F43) → G43
  248. Segment(B44, F44) → G44
  249. Segment(B45, F45) → G45
  250. Segment(B46, F46) → G46
  251. Segment(B47, F47) → G47
  252. Segment(B48, F48) → G48
  253. Segment(B49, F49) → G49
  254. Segment(B50, F50) → G50
  255. Segment(B51, F51) → G51
  256. Segment(B52, F52) → G52
  257. Segment(B53, F53) → G53
  258. Segment(B54, F54) → G54
  259. Segment(B55, F55) → G55
  260. Segment(B56, F56) → G56
  261. Segment(B57, F57) → G57
  262. Segment(B58, F58) → G58
  263. Segment(B59, F59) → G59
  264. Segment(B60, F60) → G60
  265. Segment(B61, F61) → G61
  266. Segment(B62, F62) → G62
  267. Segment(B63, F63) → G63
  268. Segment(B64, F64) → G64
  269. Segment(B65, F65) → G65
  270. Segment(B66, F66) → G66
  271. Segment(B67, F67) → G67
  272. Segment(B68, F68) → G68
  273. Segment(B69, F69) → G69
  274. Segment(B70, F70) → G70
  275. Segment(B71, F71) → G71
  276. Segment(B72, F72) → G72
  277. Segment(B73, F73) → G73
  278. Segment(B74, F74) → G74
  279. Segment(B75, F75) → G75
  280. Segment(B76, F76) → G76
  281. Segment(B77, F77) → G77
  282. Segment(B78, F78) → G78
  283. Segment(B79, F79) → G79
  284. Segment(B80, F80) → G80
  285. Segment(B81, F81) → G81
  286. Segment(B82, F82) → G82
  287. Segment(B83, F83) → G83
  288. Segment(B84, F84) → G84
  289. Segment(B85, F85) → G85
  290. Segment(B86, F86) → G86
  291. Segment(B87, F87) → G87
  292. Segment(B88, F88) → G88
  293. Segment(B89, F89) → G89
  294. Segment(B90, F90) → G90
  295. Segment(B91, F91) → G91
  296. Segment(B92, F92) → G92
  297. Segment(B93, F93) → G93
  298. Segment(B94, F94) → G94
  299. Segment(B95, F95) → G95
  300. Segment(B96, F96) → G96
  301. Segment(B97, F97) → G97
  302. Segment(B98, F98) → G98
  303. Segment(B99, F99) → G99
  304. Segment(B100, F100) → G100
  305. Segment(B101, F101) → G101
  306. Segment(B102, F102) → G102
  307. Segment(B103, F103) → G103
  308. Segment(B104, F104) → G104
  309. Segment(B105, F105) → G105
  310. Segment(B106, F106) → G106
  311. Segment(B107, F107) → G107
  312. Segment(B108, F108) → G108
  313. Segment(B109, F109) → G109
  314. Segment(B110, F110) → G110
  315. Segment(B111, F111) → G111
  316. Segment(B112, F112) → G112
  317. Segment(B113, F113) → G113
  318. Segment(B114, F114) → G114
  319. Segment(B115, F115) → G115
  320. Segment(B116, F116) → G116
  321. Segment(B117, F117) → G117
  322. Segment(B118, F118) → G118
  323. Segment(B119, F119) → G119
  324. Segment(B120, F120) → G120
  325. Segment(B121, F121) → G121
  326. Segment(B122, F122) → G122
  327. Segment(B123, F123) → G123
  328. Segment(B124, F124) → G124
  329. Segment(B125, F125) → G125
  330. Segment(B126, F126) → G126
  331. Segment(B127, F127) → G127
  332. Segment(B128, F128) → G128
  333. Segment(B129, F129) → G129
  334. Segment(B130, F130) → G130
  335. Segment(B131, F131) → G131
  336. Segment(B132, F132) → G132
  337. Segment(B133, F133) → G133
  338. Segment(B134, F134) → G134
  339. Segment(B135, F135) → G135
  340. Segment(B136, F136) → G136
  341. Segment(B137, F137) → G137
  342. Segment(B138, F138) → G138
  343. Segment(B139, F139) → G139
  344. Segment(B140, F140) → G140
  345. Segment(B141, F141) → G141
  346. Segment(B142, F142) → G142
  347. Segment(B143, F143) → G143
  348. Segment(B144, F144) → G144
  349. Segment(B145, F145) → G145
  350. Segment(B146, F146) → G146
  351. Segment(B147, F147) → G147
  352. Segment(B148, F148) → G148
  353. Segment(B149, F149) → G149
  354. Segment(B150, F150) → G150
  355. Segment(B151, F151) → G151
  356. Segment(B152, F152) → G152
  357. Segment(B153, F153) → G153
  358. Segment(B154, F154) → G154
  359. Segment(B155, F155) → G155
  360. Segment(B156, F156) → G156
  361. Segment(B157, F157) → G157
  362. Segment(B158, F158) → G158
  363. Segment(B159, F159) → G159
  364. Segment(B160, F160) → G160
  365. Segment(B161, F161) → G161
  366. Segment(B162, F162) → G162
  367. Segment(B163, F163) → G163
  368. Segment(B164, F164) → G164
  369. Segment(B165, F165) → G165
  370. Segment(B166, F166) → G166
  371. Segment(B167, F167) → G167
  372. Segment(B168, F168) → G168
  373. Segment(B169, F169) → G169
  374. Segment(B170, F170) → G170
  375. Segment(B171, F171) → G171
  376. Segment(B172, F172) → G172
  377. Segment(B173, F173) → G173
  378. Segment(B174, F174) → G174
  379. Segment(B175, F175) → G175
  380. Segment(B176, F176) → G176
  381. Segment(B177, F177) → G177
  382. Segment(B178, F178) → G178
  383. Segment(B179, F179) → G179
  384. Segment(B180, F180) → G180
  385. Segment(B181, F181) → G181
  386. Segment(B182, F182) → G182
  387. Segment(B183, F183) → G183
  388. Segment(B184, F184) → G184
  389. Segment(B185, F185) → G185
  390. Segment(B186, F186) → G186
  391. Segment(B187, F187) → G187
  392. Segment(B188, F188) → G188
  393. Segment(B189, F189) → G189
  394. Segment(B190, F190) → G190
  395. Segment(B191, F191) → G191
  396. Segment(B192, F192) → G192
  397. Segment(B193, F193) → G193
  398. Segment(B194, F194) → G194
  399. Segment(B195, F195) → G195
  400. Segment(B196, F196) → G196
  401. Segment(B197, F197) → G197
  402. Segment(B198, F198) → G198
  403. Segment(B199, F199) → G199
  404. Segment(B200, F200) → G200
  405. Textfield(f) → inputBox1
  406. Textfield(g) → inputBox2