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Function Diagrams: Visualizing Function Mappings with Similar Triangles and Tran

Function Diagrams: Visualizing Function Mappings with Similar Triangles and Tran
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2018-09-19 02:13
TriangleFunctionTransformationGeometric ConstructionGraphing
① This GeoGebra example, titled "Function Diagrams," demonstrates a dynamic diagram that visualizes the correspondence between the domain and range of a function f, using similar triangles and geometric transformations (translation) to aid understanding. ② Core mathematical concepts include function graphs, similar triangles, geometric transformations (translation), and the visual representation of function values, involving basic geometric elements such as points, segments, and intersections. ③ Construction highlights: From the construction summary, commands such as Intersect, Point, Line, Segment, and Textfield are used, with objects like width, f, start, A1~A25, B1~B7 defined. The diagram is built from numerous points and segments, likely incorporating adjustable parameters (e.g., width) and dynamic text input. ④ This is suitable for middle or high school students learning function concepts, geometric transformations, and similar triangles, and can be used for classroom demonstrations or student exploration of function properties.

GeoGebra Commands & Parameters

  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