63:@0.942772:0.974518:0.963274:0.974518:0.963274:0.956333:0.942772:0.956333:0.000000:0.000000 Pensamiento espacial, numérico y variacional:@0.500422:0.043661:0.926919:0.043661:0.926919:0.024916:0.500422:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Gráfico de funciones exponenciales con GeoGebra:@0.073089:0.136836:0.467998:0.136836:0.467998:0.119889:0.073089:0.119889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. Grafica:@0.073089:0.164198:0.156646:0.164199:0.156646:0.147530:0.073089:0.147529:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.086342:0.164199:0.090373:0.164199:0.090373:0.148487:0.086342:0.148487:0.000000 una función ( ) :@0.156646:0.164199:0.298216:0.164199:0.298216:0.148487:0.156646:0.148487:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.252916:0.164199:0.269943:0.164199:0.269943:0.148764:0.252916:0.148764:0.000000:0.000000:0.000000 5:@0.278852:0.163645:0.294185:0.163645:0.294185:0.149929:0.278852:0.149929:0.000000 a a:@0.298216:0.164199:0.331018:0.164199:0.331018:0.148764:0.298216:0.148764:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.307472:0.158135:0.311819:0.158135:0.311819:0.149137:0.307472:0.149137:0.000000 1. Luego, :@0.331018:0.164199:0.423973:0.164199:0.423973:0.148487:0.331018:0.148487:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.335050:0.163645:0.350383:0.163645:0.350383:0.149929:0.335050:0.149929:0.000000 realiza:@0.423973:0.164199:0.473305:0.164199:0.473305:0.147530:0.423973:0.147530:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 los desplazamientos horizontales y verticales. :@0.473305:0.164199:0.811665:0.164199:0.811665:0.148487:0.473305:0.148487:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.073089:0.180841:0.077120:0.180841:0.077120:0.165129:0.073089:0.165129:0.000000 f x:@0.103210:0.180841:0.120237:0.180841:0.120237:0.165406:0.103210:0.165406:0.000000:0.000000:0.000000 ( ) :@0.107904:0.180841:0.148510:0.180841:0.148510:0.165129:0.107904:0.165129:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.129146:0.180287:0.144479:0.180287:0.144479:0.166571:0.129146:0.166571:0.000000 a:@0.148510:0.180841:0.157769:0.180841:0.157769:0.165406:0.148510:0.165406:0.000000 ( ):@0.157768:0.174777:0.186839:0.174777:0.186839:0.165617:0.157768:0.165617:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.160611:0.174777:0.164958:0.174777:0.164958:0.165779:0.160611:0.165779:0.000000 1:@0.167308:0.174454:0.176247:0.174454:0.176247:0.166458:0.167308:0.166458:0.000000 b:@0.178597:0.174777:0.183995:0.174777:0.183995:0.165779:0.178597:0.165779:0.000000 , ( ) .:@0.186839:0.180841:0.292865:0.180841:0.292865:0.165129:0.186839:0.165129:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.198105:0.180841:0.215131:0.180841:0.215131:0.165406:0.198105:0.165406:0.000000:0.000000:0.000000 5:@0.224041:0.180287:0.239374:0.180287:0.239374:0.166571:0.224041:0.166571:0.000000 a:@0.243405:0.180841:0.252664:0.180841:0.252664:0.165406:0.243405:0.165406:0.000000 x:@0.252662:0.174777:0.257008:0.174777:0.257008:0.165779:0.252662:0.165779:0.000000 1:@0.261039:0.180287:0.276372:0.180287:0.276372:0.166571:0.261039:0.166571:0.000000 b:@0.280404:0.180841:0.289662:0.180841:0.289662:0.165406:0.280404:0.165406:0.000000 :@0.073089:0.197483:0.077120:0.197483:0.077120:0.181770:0.073089:0.181770:0.000000 Sea la función ( ) 5 , :@0.103203:0.197483:0.275519:0.197483:0.275519:0.181770:0.103203:0.181770:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.209658:0.197483:0.226684:0.197483:0.226684:0.182048:0.209658:0.182048:0.000000:0.000000:0.000000 5:@0.235594:0.196928:0.250927:0.196928:0.250927:0.183213:0.235594:0.183213:0.000000 x:@0.263939:0.191419:0.268285:0.191419:0.268285:0.182420:0.263939:0.182420:0.000000 analiza:@0.275519:0.197483:0.328882:0.197483:0.328882:0.180814:0.275519:0.180814:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 su gráfica.:@0.328882:0.197483:0.405916:0.197483:0.405916:0.181770:0.328882:0.181770:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Traza:@0.400633:0.530514:0.440503:0.530514:0.440503:0.513844:0.400633:0.513844:0.000000:0.000000:0.000000:0.000000:0.000000 las gráficas de ( ) 5 2 y de ( ) 5:@0.440503:0.530514:0.758686:0.530509:0.758686:0.514796:0.440503:0.514801:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.556266:0.530514:0.573293:0.530514:0.573293:0.515079:0.556266:0.515079:0.000000:0.000000:0.000000 5:@0.583601:0.529959:0.598934:0.529959:0.598934:0.516244:0.583601:0.516244:0.000000 x:@0.613341:0.524445:0.617687:0.524445:0.617687:0.515446:0.613341:0.515446:0.000000 1:@0.623116:0.529954:0.638450:0.529954:0.638450:0.516239:0.623116:0.516239:0.000000 f x:@0.701605:0.530509:0.718632:0.530509:0.718632:0.515074:0.701605:0.515074:0.000000:0.000000:0.000000 5:@0.728940:0.529954:0.744273:0.529954:0.744273:0.516239:0.728940:0.516239:0.000000 ( 2):@0.758666:0.524445:0.789207:0.524445:0.789207:0.515285:0.758666:0.515285:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.761510:0.524445:0.765856:0.524445:0.765856:0.515446:0.761510:0.515446:0.000000 1:@0.769022:0.524122:0.777961:0.524122:0.777961:0.516125:0.769022:0.516125:0.000000 . :@0.789202:0.530509:0.796436:0.530509:0.796436:0.514796:0.789202:0.514796:0.000000:0.000000 Analiza:@0.797835:0.530509:0.853535:0.530509:0.853535:0.513839:0.797835:0.513839:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 qué :@0.853535:0.530509:0.891675:0.530509:0.891675:0.514796:0.853535:0.514796:0.000000:0.000000:0.000000:0.000000:0.000000 sucede en cada caso.:@0.400643:0.547151:0.555281:0.547151:0.555281:0.531438:0.400643:0.531438:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2.:@0.144493:0.830015:0.157144:0.830015:0.157144:0.814103:0.144493:0.814103:0.000000:0.000000 La función ( ) 5 2 se desplazó dos uni-:@0.157142:0.830015:0.471038:0.830015:0.471038:0.815017:0.157142:0.815017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.238263:0.830015:0.254515:0.830015:0.254515:0.815282:0.238263:0.815282:0.000000:0.000000:0.000000 5:@0.263020:0.829486:0.277656:0.829486:0.277656:0.816394:0.263020:0.816394:0.000000 x:@0.290077:0.824226:0.294226:0.824226:0.294226:0.815637:0.290077:0.815637:0.000000 1:@0.298074:0.829486:0.312710:0.829486:0.312710:0.816394:0.298074:0.816394:0.000000 dades hacia arriba, al igual que su asíntota, :@0.161094:0.845901:0.465750:0.845901:0.465750:0.830902:0.161094:0.830902:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.161094:0.861786:0.168227:0.861786:0.168227:0.847052:0.161094:0.847052:0.000000 2. La función sigue siendo creciente.:@0.168227:0.861786:0.443136:0.861786:0.443136:0.846788:0.168227:0.846788:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.172075:0.861257:0.186711:0.861257:0.186711:0.848164:0.172075:0.848164:0.000000 3.:@0.535254:0.830015:0.547904:0.830015:0.547904:0.814103:0.535254:0.814103:0.000000:0.000000 La función ( ) 5:@0.547904:0.830015:0.680841:0.830015:0.680841:0.815017:0.547904:0.815017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.629025:0.830015:0.645278:0.830015:0.645278:0.815282:0.629025:0.815282:0.000000:0.000000:0.000000 5:@0.653782:0.829486:0.668418:0.829486:0.668418:0.816394:0.653782:0.816394:0.000000 ( 2):@0.680840:0.824226:0.708436:0.824226:0.708436:0.815482:0.680840:0.815482:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.683555:0.824226:0.687703:0.824226:0.687703:0.815637:0.683555:0.815637:0.000000 1:@0.689947:0.823918:0.698479:0.823918:0.698479:0.816285:0.689947:0.816285:0.000000 se desplazó dos uni-:@0.708436:0.830015:0.854342:0.830015:0.854342:0.815017:0.708436:0.815017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 dades a la izquierda, y la asíntota se mantiene :@0.551865:0.845901:0.873142:0.845901:0.873142:0.830902:0.551865:0.830902:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en 0. La función sigue siendo creciente.:@0.551865:0.861786:0.859541:0.861786:0.859541:0.846788:0.551865:0.846788:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.577500:0.861786:0.584634:0.861786:0.584634:0.847052:0.577500:0.847052:0.000000 5:@0.588482:0.861257:0.603118:0.861257:0.603118:0.848164:0.588482:0.848164:0.000000 1. En la barra de :@0.144493:0.236902:0.266142:0.236902:0.266142:0.221189:0.144493:0.221189:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Entrada:@0.265964:0.236902:0.321211:0.236902:0.321211:0.221466:0.265964:0.221466:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , :@0.321186:0.236902:0.328420:0.236902:0.328420:0.221189:0.321186:0.221189:0.000000:0.000000 ingresa:@0.163472:0.253543:0.218943:0.253543:0.218943:0.236874:0.163472:0.236874:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la función ( ) 5 .:@0.218841:0.253543:0.359568:0.253543:0.359568:0.237831:0.218841:0.237831:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.298397:0.253543:0.315277:0.253543:0.315277:0.238108:0.298397:0.238108:0.000000:0.000000:0.000000 5:@0.323947:0.252989:0.339280:0.252989:0.339280:0.239273:0.323947:0.239273:0.000000 x:@0.352058:0.247479:0.356404:0.247479:0.356404:0.238481:0.352058:0.238481:0.000000 2. La gráfica de la función :@0.144493:0.290508:0.334638:0.290508:0.334638:0.274796:0.144493:0.274796:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.163469:0.307150:0.180348:0.307150:0.180348:0.291715:0.163469:0.291715:0.000000:0.000000:0.000000 ( ) 5 es creciente, :@0.168089:0.307150:0.319077:0.307150:0.319077:0.291438:0.168089:0.291438:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.189018:0.306596:0.204351:0.306596:0.204351:0.292880:0.189018:0.292880:0.000000 x:@0.217121:0.301086:0.221467:0.301086:0.221467:0.292088:0.217121:0.292088:0.000000 porque > 1.:@0.163464:0.323792:0.260894:0.323792:0.260894:0.308079:0.163464:0.308079:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.220784:0.323792:0.230043:0.323792:0.230043:0.308357:0.220784:0.308357:0.000000 3. La función tiene asíntota :@0.144493:0.357620:0.346218:0.357620:0.346218:0.341908:0.144493:0.341908:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 horizontal en 0.:@0.163466:0.374262:0.305809:0.374262:0.305809:0.358550:0.163466:0.358550:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.263141:0.374262:0.270614:0.374262:0.270614:0.358827:0.263141:0.358827:0.000000 5:@0.274498:0.373708:0.289831:0.373708:0.289831:0.359992:0.274498:0.359992:0.000000 Practica:@0.139749:0.883647:0.197310:0.883647:0.197310:0.867735:0.139749:0.867735:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las gráficas de funciones exponenciales con los ejercicios de la página 114 de este texto.:@0.197310:0.883647:0.814894:0.883647:0.814894:0.868649:0.197310:0.868649:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Competencia digital :@0.117786:0.096815:0.407670:0.096815:0.407670:0.068698:0.117786:0.068698:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000