34:@0.058783:0.510692:0.077690:0.510692:0.077690:0.494068:0.058783:0.494068:0.000000:0.000000
Tema:@0.047190:0.135475:0.083321:0.135475:0.083321:0.113749:0.047190:0.113749:0.000000:0.000000:0.000000:0.000000
1. :@0.115209:0.759280:0.133950:0.759280:0.133950:0.742145:0.115209:0.742145:0.000000:0.000000:0.000000
Sean :@0.148452:0.759280:0.187574:0.759280:0.187574:0.742891:0.148452:0.742891:0.000000:0.000000:0.000000:0.000000:0.000000
():@0.196553:0.762363:0.220546:0.762363:0.220546:0.741962:0.196553:0.741962:0.000000:0.000000
():@0.345025:0.762363:0.369018:0.762363:0.369018:0.741962:0.345025:0.741962:0.000000:0.000000
=:@0.223200:0.760491:0.233316:0.760491:0.233316:0.744918:0.223200:0.744918:0.000000
≠:@0.296763:0.760491:0.306880:0.760491:0.306880:0.744918:0.296763:0.744918:0.000000
=:@0.371668:0.760491:0.381785:0.760491:0.381785:0.744918:0.371668:0.744918:0.000000
≠ ±:@0.459052:0.760491:0.483294:0.760491:0.483294:0.744918:0.459052:0.744918:0.000000:0.000000:0.000000
1:@0.251843:0.750851:0.260836:0.750851:0.260836:0.734462:0.251843:0.734462:0.000000
–4:@0.250893:0.770304:0.272343:0.770304:0.272343:0.753915:0.250893:0.753915:0.000000:0.000000
,:@0.275866:0.759813:0.279072:0.759813:0.279072:0.743424:0.275866:0.743424:0.000000
.:@0.279994:0.759813:0.283200:0.759813:0.283200:0.743424:0.279994:0.743424:0.000000
4;:@0.310878:0.759813:0.323980:0.759813:0.323980:0.743424:0.310878:0.743424:0.000000:0.000000
...:@0.324902:0.759813:0.334189:0.759813:0.334189:0.743424:0.324902:0.743424:0.000000:0.000000:0.000000
1:@0.407200:0.750851:0.416192:0.750851:0.416192:0.734462:0.407200:0.734462:0.000000
–16:@0.406638:0.770304:0.434999:0.770304:0.434999:0.753915:0.406638:0.753915:0.000000:0.000000:0.000000
,:@0.438155:0.759813:0.441361:0.759813:0.441361:0.743424:0.438155:0.743424:0.000000
.:@0.442283:0.759813:0.445489:0.759813:0.445489:0.743424:0.442283:0.743424:0.000000
4, desarrolla las operaciones solicitadas en cada inciso.:@0.483123:0.759813:0.868765:0.759274:0.868765:0.742885:0.483123:0.743424:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.397111:0.762642:0.402323:0.762642:0.402323:0.753144:0.397111:0.753144:0.000000
fx:@0.188177:0.759813:0.212336:0.759813:0.212336:0.743452:0.188177:0.743452:0.000000:0.000000
x:@0.239535:0.770311:0.246998:0.770311:0.246998:0.753949:0.239535:0.753949:0.000000
x:@0.284870:0.759813:0.292334:0.759813:0.292334:0.743452:0.284870:0.743452:0.000000
g x:@0.335122:0.759813:0.360811:0.759813:0.360811:0.743452:0.335122:0.743452:0.000000:0.000000:0.000000
x:@0.388001:0.770304:0.395465:0.770304:0.395465:0.753943:0.388001:0.753943:0.000000
x:@0.447159:0.759813:0.454622:0.759813:0.454622:0.743452:0.447159:0.743452:0.000000
Taller:@0.175844:0.707575:0.236739:0.707575:0.236739:0.673628:0.175844:0.673628:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
I.M.5.3.1. Grafica funciones reales y analiza su dominio, recorrido, monotonía, ceros, extremos, paridad; identifica las funciones afines, :@0.256865:0.685039:0.877673:0.685039:0.877673:0.674610:0.256865:0.674610:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
potencia, raíz cuadrada, valor absoluto; reconoce si una función es inyectiva, sobreyectiva o biyectiva; realiza operaciones con :@0.256865:0.695601:0.877758:0.695601:0.877758:0.685171:0.256865:0.685171:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
funciones aplicando las propiedades de los números reales en problemas reales e hipotéticos. (I.4.):@0.256865:0.706162:0.714621:0.706162:0.714621:0.695733:0.256865:0.695733:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Actividad resuelta:@0.115209:0.406528:0.272331:0.406528:0.272331:0.388091:0.115209:0.388091:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean las funciones racionales: :@0.115209:0.452869:0.335216:0.452869:0.335216:0.436480:0.115209:0.436480:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.486769:0.436817:0.500073:0.436817:0.500073:0.420068:0.486769:0.420068:0.000000
:@0.485515:0.473550:0.498820:0.473550:0.498820:0.456801:0.485515:0.456801:0.000000
():@0.355787:0.439077:0.378987:0.439077:0.378987:0.419144:0.355787:0.419144:0.000000:0.000000
():@0.358035:0.475810:0.381235:0.475810:0.381235:0.455877:0.358035:0.455877:0.000000:0.000000
{}:@0.514045:0.438388:0.549592:0.438388:0.549592:0.420012:0.514045:0.420012:0.000000:0.000000
{}:@0.512792:0.475124:0.534886:0.475124:0.534886:0.456748:0.512792:0.456748:0.000000:0.000000
=:@0.381647:0.436623:0.391764:0.436623:0.391764:0.421050:0.381647:0.421050:0.000000
+:@0.407833:0.447549:0.417950:0.447549:0.417950:0.431976:0.407833:0.431976:0.000000
∀ ∈:@0.445370:0.436623:0.483430:0.436623:0.483430:0.421050:0.445370:0.421050:0.000000:0.000000:0.000000
=:@0.383914:0.473356:0.394031:0.473356:0.394031:0.457783:0.383914:0.457783:0.000000
∀ ∈:@0.444117:0.473356:0.482177:0.473356:0.482177:0.457783:0.444117:0.457783:0.000000:0.000000:0.000000
⎧:@0.337845:0.426997:0.346948:0.426997:0.346948:0.411424:0.337845:0.411424:0.000000
⎨:@0.337845:0.454575:0.346948:0.454575:0.346948:0.439002:0.337845:0.439002:0.000000
⎪:@0.337845:0.440468:0.346948:0.440468:0.346948:0.424895:0.337845:0.424895:0.000000
⎪:@0.337845:0.444077:0.346948:0.444077:0.346948:0.428505:0.337845:0.428505:0.000000
⎩:@0.337845:0.482498:0.346948:0.482498:0.346948:0.466925:0.337845:0.466925:0.000000
⎪:@0.337845:0.468032:0.346948:0.468032:0.346948:0.452459:0.337845:0.452459:0.000000
⎪:@0.337845:0.479856:0.346948:0.479856:0.346948:0.464284:0.337845:0.464284:0.000000
3:@0.408109:0.427398:0.417102:0.427398:0.417102:0.411728:0.408109:0.411728:0.000000
2:@0.419995:0.446844:0.428988:0.446844:0.428988:0.431174:0.419995:0.431174:0.000000
,:@0.431770:0.435918:0.434977:0.435918:0.434977:0.420248:0.431770:0.420248:0.000000
...:@0.435898:0.435918:0.445186:0.435918:0.445186:0.420248:0.435898:0.420248:0.000000:0.000000:0.000000
– –2 ,:@0.503122:0.435918:0.553865:0.435918:0.553865:0.420248:0.503122:0.420248:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.408367:0.464131:0.417360:0.464131:0.417360:0.448462:0.408367:0.448462:0.000000
–1:@0.410873:0.483577:0.430444:0.483577:0.430444:0.467907:0.410873:0.467907:0.000000:0.000000
,:@0.430499:0.472651:0.433705:0.472651:0.433705:0.456981:0.430499:0.456981:0.000000
...:@0.434627:0.472651:0.443914:0.472651:0.443914:0.456981:0.434627:0.456981:0.000000:0.000000:0.000000
–1:@0.501851:0.472651:0.529382:0.472651:0.529382:0.456981:0.501851:0.456981:0.000000:0.000000
fx:@0.347003:0.435918:0.371162:0.435918:0.371162:0.420524:0.347003:0.420524:0.000000:0.000000
x:@0.397255:0.446844:0.404719:0.446844:0.404719:0.431450:0.397255:0.431450:0.000000
x:@0.458398:0.435918:0.465862:0.435918:0.465862:0.420524:0.458398:0.420524:0.000000
gx:@0.347722:0.472651:0.373410:0.472651:0.373410:0.457258:0.347722:0.457258:0.000000:0.000000
x:@0.399504:0.483577:0.406967:0.483577:0.406967:0.468184:0.399504:0.468184:0.000000
x:@0.457145:0.472651:0.464608:0.472651:0.464608:0.457258:0.457145:0.457258:0.000000
Efectuemos:@0.115209:0.508954:0.205412:0.508954:0.205412:0.492330:0.115209:0.492330:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 las siguientes operaciones:  ( ) +  ( ),  ( ) –  ( ),  ( ) ·  ( ):@0.205412:0.508954:0.616162:0.508954:0.616162:0.492565:0.205412:0.492565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.408778:0.508954:0.425823:0.508954:0.425823:0.492593:0.408778:0.492593:0.000000:0.000000:0.000000
g x f x:@0.449761:0.508954:0.500547:0.508954:0.500547:0.492593:0.449761:0.492593:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g x f x g x:@0.522716:0.508954:0.611279:0.508954:0.611279:0.492593:0.522716:0.492593:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a) :@0.115209:0.542133:0.133931:0.542133:0.133931:0.525232:0.115209:0.525232:0.000000:0.000000:0.000000
():@0.159862:0.544611:0.183063:0.544611:0.183063:0.524678:0.159862:0.524678:0.000000:0.000000
():@0.207977:0.544611:0.231177:0.544611:0.231177:0.524678:0.207977:0.524678:0.000000:0.000000
(:@0.345613:0.555534:0.351749:0.555534:0.351749:0.535600:0.345613:0.535600:0.000000
)(:@0.385398:0.555534:0.398753:0.555535:0.398753:0.535601:0.385398:0.535600:0.000000:0.000000
):@0.428901:0.555535:0.435037:0.555535:0.435037:0.535601:0.428901:0.535601:0.000000
+:@0.184781:0.542157:0.194898:0.542157:0.194898:0.526584:0.184781:0.526584:0.000000
=:@0.233836:0.542157:0.243953:0.542157:0.243953:0.526584:0.233836:0.526584:0.000000
+:@0.260003:0.553083:0.270120:0.553083:0.270120:0.537510:0.260003:0.537510:0.000000
+:@0.284180:0.542157:0.294297:0.542157:0.294297:0.526584:0.284180:0.526584:0.000000
=:@0.331447:0.542157:0.341564:0.542157:0.341564:0.526584:0.331447:0.526584:0.000000
+:@0.391927:0.533638:0.402043:0.533638:0.402043:0.518065:0.391927:0.518065:0.000000
+:@0.364082:0.553083:0.374199:0.553083:0.374199:0.537510:0.364082:0.537510:0.000000
3:@0.260261:0.532960:0.269254:0.532960:0.269254:0.516571:0.260261:0.516571:0.000000
2:@0.272147:0.552405:0.281140:0.552405:0.281140:0.536016:0.272147:0.536016:0.000000
2:@0.308118:0.532960:0.317110:0.532960:0.317110:0.516571:0.308118:0.516571:0.000000
–1:@0.310624:0.552405:0.330194:0.552405:0.330194:0.536016:0.310624:0.536016:0.000000:0.000000
5:@0.371509:0.532960:0.380501:0.532960:0.380501:0.516571:0.371509:0.516571:0.000000
1:@0.402928:0.532960:0.411921:0.532960:0.411921:0.516571:0.402928:0.516571:0.000000
2:@0.376230:0.552403:0.385222:0.552403:0.385222:0.536014:0.376230:0.536014:0.000000
–1:@0.411887:0.552403:0.431449:0.552403:0.431449:0.536014:0.411887:0.536014:0.000000:0.000000
fx:@0.151072:0.541477:0.175231:0.541477:0.175231:0.525116:0.151072:0.525116:0.000000:0.000000
gx:@0.197657:0.541477:0.223345:0.541477:0.223345:0.525116:0.197657:0.525116:0.000000:0.000000
x:@0.249439:0.552403:0.256902:0.552403:0.256902:0.536041:0.249439:0.536041:0.000000
x:@0.299286:0.552403:0.306749:0.552403:0.306749:0.536041:0.299286:0.536041:0.000000
x:@0.381362:0.532957:0.388826:0.532957:0.388826:0.516596:0.381362:0.516596:0.000000
x:@0.353510:0.552403:0.360973:0.552403:0.360973:0.536041:0.353510:0.536041:0.000000
x:@0.400519:0.552403:0.407982:0.552403:0.407982:0.536041:0.400519:0.536041:0.000000
b) :@0.115209:0.587063:0.135240:0.587063:0.135240:0.570162:0.115209:0.570162:0.000000:0.000000:0.000000
():@0.159862:0.591452:0.183063:0.591452:0.183063:0.571518:0.159862:0.571518:0.000000:0.000000
():@0.208345:0.591452:0.231546:0.591452:0.231546:0.571518:0.208345:0.571518:0.000000:0.000000
(:@0.346350:0.602375:0.352486:0.602375:0.352486:0.582441:0.346350:0.582441:0.000000
)(:@0.386135:0.602375:0.399485:0.602374:0.399485:0.582441:0.386135:0.582441:0.000000:0.000000
):@0.429633:0.602374:0.435769:0.602374:0.435769:0.582441:0.429633:0.582441:0.000000
=:@0.234201:0.588998:0.244318:0.588998:0.244318:0.573425:0.234201:0.573425:0.000000
+:@0.260368:0.599924:0.270485:0.599924:0.270485:0.584351:0.260368:0.584351:0.000000
=:@0.332199:0.588998:0.342316:0.588998:0.342316:0.573425:0.332199:0.573425:0.000000
+:@0.364816:0.599924:0.374933:0.599924:0.374933:0.584351:0.364816:0.584351:0.000000
–:@0.185570:0.588320:0.194784:0.588320:0.194784:0.571931:0.185570:0.571931:0.000000
3:@0.260645:0.579801:0.269637:0.579801:0.269637:0.563412:0.260645:0.563412:0.000000
2:@0.272531:0.599246:0.281523:0.599246:0.281523:0.582857:0.272531:0.582857:0.000000
–:@0.285356:0.588320:0.294570:0.588320:0.294570:0.571931:0.285356:0.571931:0.000000
2:@0.308870:0.579801:0.317862:0.579801:0.317862:0.563412:0.308870:0.563412:0.000000
–1:@0.311376:0.599246:0.330946:0.599246:0.330946:0.582857:0.311376:0.582857:0.000000:0.000000
–7:@0.387187:0.579801:0.407495:0.579801:0.407495:0.563412:0.387187:0.563412:0.000000:0.000000
2:@0.376963:0.599242:0.385956:0.599242:0.385956:0.582853:0.376963:0.582853:0.000000
–1:@0.412621:0.599242:0.432183:0.599242:0.432183:0.582853:0.412621:0.582853:0.000000:0.000000
fx:@0.151069:0.588316:0.175228:0.588316:0.175228:0.571955:0.151069:0.571955:0.000000:0.000000
gx:@0.198023:0.588316:0.223711:0.588316:0.223711:0.571955:0.198023:0.571955:0.000000:0.000000
x:@0.249804:0.599242:0.257267:0.599242:0.257267:0.582881:0.249804:0.582881:0.000000
x:@0.300001:0.599242:0.307464:0.599242:0.307464:0.582881:0.300001:0.582881:0.000000
x:@0.375812:0.579797:0.383276:0.579797:0.383276:0.563436:0.375812:0.563436:0.000000
x:@0.354242:0.599242:0.361705:0.599242:0.361705:0.582881:0.354242:0.582881:0.000000
x:@0.401251:0.599242:0.408714:0.599242:0.408714:0.582881:0.401251:0.582881:0.000000
c) :@0.115209:0.629689:0.132844:0.629689:0.132844:0.612788:0.115209:0.612788:0.000000:0.000000:0.000000
() ():@0.159862:0.632822:0.225409:0.632822:0.225409:0.612889:0.159862:0.612889:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.334077:0.643745:0.340214:0.643745:0.340214:0.623811:0.334077:0.623811:0.000000
)(:@0.373862:0.643745:0.387236:0.643744:0.387236:0.623811:0.373862:0.623811:0.000000:0.000000
):@0.417383:0.643744:0.423520:0.643744:0.423520:0.623811:0.417383:0.623811:0.000000
⋅:@0.184781:0.630367:0.189388:0.630367:0.189388:0.614794:0.184781:0.614794:0.000000
=:@0.228068:0.630367:0.238185:0.630367:0.238185:0.614794:0.228068:0.614794:0.000000
+:@0.254254:0.641293:0.264370:0.641293:0.264370:0.625720:0.254254:0.625720:0.000000
⋅:@0.278431:0.630367:0.283038:0.630367:0.283038:0.614794:0.278431:0.614794:0.000000
=:@0.319948:0.630367:0.330065:0.630367:0.330065:0.614794:0.319948:0.614794:0.000000
+:@0.352565:0.641293:0.362682:0.641293:0.362682:0.625720:0.352565:0.625720:0.000000
3:@0.254512:0.621170:0.263504:0.621170:0.263504:0.604781:0.254512:0.604781:0.000000
2:@0.266397:0.640615:0.275390:0.640615:0.275390:0.624226:0.266397:0.624226:0.000000
2:@0.296600:0.621170:0.305593:0.621170:0.305593:0.604781:0.296600:0.604781:0.000000
–1:@0.299107:0.640615:0.318677:0.640615:0.318677:0.624226:0.299107:0.624226:0.000000:0.000000
6:@0.374328:0.621170:0.383321:0.621170:0.383321:0.604781:0.374328:0.604781:0.000000
2:@0.364712:0.640612:0.373705:0.640612:0.373705:0.624224:0.364712:0.624224:0.000000
–1:@0.400370:0.640612:0.419931:0.640612:0.419931:0.624224:0.400370:0.624224:0.000000:0.000000
fx gx:@0.151072:0.629687:0.217596:0.629687:0.217596:0.613325:0.151072:0.613325:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.243690:0.640612:0.251153:0.640612:0.251153:0.624251:0.243690:0.624251:0.000000
x:@0.287768:0.640612:0.295232:0.640612:0.295232:0.624251:0.287768:0.624251:0.000000
x:@0.341993:0.640612:0.349456:0.640612:0.349456:0.624251:0.341993:0.624251:0.000000
x:@0.389002:0.640612:0.396465:0.640612:0.396465:0.624251:0.389002:0.624251:0.000000
Operaciones con funciones racionales:@0.115891:0.141978:0.668066:0.141978:0.668066:0.101242:0.115891:0.101242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M. 5.1.45. Realizar operaciones de suma y multiplicación entre funciones racionales y de multiplicación de números reales por funciones racionales en ejercicios :@0.125388:0.069719:0.877758:0.069719:0.877758:0.059289:0.125388:0.059289:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
algebraicos, para simplificar las funciones.:@0.125388:0.080280:0.319050:0.080280:0.319050:0.069851:0.125388:0.069851:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
8:@0.054138:0.122645:0.076372:0.122645:0.076372:0.065614:0.054138:0.065614:0.000000
Operaciones con funciones racionales:@0.347792:0.169495:0.647459:0.169495:0.647459:0.152595:0.347792:0.152595:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Adición de funciones racionales:@0.122478:0.206492:0.373956:0.206492:0.373956:0.189591:0.122478:0.189591:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+= +=:@0.566229:0.205121:0.654147:0.205121:0.654147:0.189548:0.566229:0.189548:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.677108:0.196602:0.687224:0.196602:0.687224:0.181029:0.677108:0.181029:0.000000
≠:@0.725115:0.205121:0.735232:0.205121:0.735232:0.189548:0.725115:0.189548:0.000000
≠:@0.761823:0.205121:0.771940:0.205121:0.771940:0.189548:0.761823:0.189548:0.000000
,:@0.708311:0.204443:0.711517:0.204443:0.711517:0.188055:0.708311:0.188055:0.000000
0,:@0.737776:0.204443:0.750518:0.204443:0.750518:0.188055:0.737776:0.188055:0.000000:0.000000
0.:@0.774474:0.204443:0.786482:0.204443:0.786482:0.188055:0.774474:0.188055:0.000000:0.000000
fg:@0.556800:0.204443:0.588367:0.204443:0.588367:0.188082:0.556800:0.188082:0.000000:0.000000
p r:@0.606223:0.195924:0.638472:0.195924:0.638472:0.179563:0.606223:0.179563:0.000000:0.000000:0.000000
q s:@0.606020:0.215369:0.639356:0.215369:0.639356:0.199008:0.606020:0.199008:0.000000:0.000000:0.000000
ps qr:@0.659258:0.195924:0.704129:0.195924:0.704129:0.179563:0.659258:0.179563:0.000000:0.000000:0.000000:0.000000:0.000000
qs:@0.673871:0.215369:0.689461:0.215369:0.689461:0.199008:0.673871:0.199008:0.000000:0.000000
q:@0.713232:0.204443:0.722502:0.204443:0.722502:0.188082:0.713232:0.188082:0.000000
s:@0.752244:0.204443:0.758620:0.204443:0.758620:0.188082:0.752244:0.188082:0.000000
Resta de funciones racionales:@0.122479:0.255519:0.356691:0.255519:0.356691:0.238618:0.122479:0.238618:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.591357:0.254156:0.601474:0.254156:0.601474:0.238583:0.591357:0.238583:0.000000
=:@0.644760:0.254156:0.654877:0.254156:0.654877:0.238583:0.644760:0.238583:0.000000
≠:@0.726214:0.254156:0.736331:0.254156:0.736331:0.238583:0.726214:0.238583:0.000000
≠:@0.762922:0.254156:0.773039:0.254156:0.773039:0.238583:0.762922:0.238583:0.000000
–:@0.567014:0.253478:0.576228:0.253478:0.576228:0.237089:0.567014:0.237089:0.000000
–:@0.620159:0.253478:0.629373:0.253478:0.629373:0.237089:0.620159:0.237089:0.000000
–:@0.678630:0.244959:0.687844:0.244959:0.687844:0.228570:0.678630:0.228570:0.000000
,:@0.709405:0.253478:0.712611:0.253478:0.712611:0.237089:0.709405:0.237089:0.000000
0,:@0.738870:0.253478:0.751617:0.253478:0.751617:0.237089:0.738870:0.237089:0.000000:0.000000
0.:@0.775573:0.253478:0.787583:0.253478:0.787583:0.237089:0.775573:0.237089:0.000000:0.000000
fg:@0.556814:0.253478:0.588749:0.253478:0.588749:0.237117:0.556814:0.237117:0.000000:0.000000
p r:@0.606605:0.244959:0.639222:0.244959:0.639222:0.228597:0.606605:0.228597:0.000000:0.000000:0.000000
q s:@0.606402:0.264404:0.640107:0.264404:0.640107:0.248043:0.606402:0.248043:0.000000:0.000000:0.000000
ps qr:@0.660008:0.244959:0.705248:0.244959:0.705248:0.228597:0.660008:0.228597:0.000000:0.000000:0.000000:0.000000:0.000000
qs:@0.674824:0.264404:0.690414:0.264404:0.690414:0.248043:0.674824:0.248043:0.000000:0.000000
q:@0.714352:0.253478:0.723621:0.253478:0.723621:0.237117:0.714352:0.237117:0.000000
s:@0.753363:0.253478:0.759739:0.253478:0.759739:0.237117:0.753363:0.237117:0.000000
Multiplicación de funciones racionales:@0.122493:0.304554:0.426582:0.304554:0.426582:0.287653:0.122493:0.287653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=⋅ =:@0.573296:0.303191:0.630680:0.303191:0.630680:0.287618:0.573296:0.287618:0.000000:0.000000:0.000000:0.000000
≠:@0.671295:0.303191:0.681411:0.303191:0.681411:0.287618:0.671295:0.287618:0.000000
≠:@0.707984:0.303191:0.718101:0.303191:0.718101:0.287618:0.707984:0.287618:0.000000
,:@0.654489:0.302513:0.657695:0.302513:0.657695:0.286124:0.654489:0.286124:0.000000
0,:@0.683954:0.302513:0.696701:0.302513:0.696701:0.286124:0.683954:0.286124:0.000000:0.000000
0.:@0.720657:0.302513:0.732665:0.302513:0.732665:0.286124:0.720657:0.286124:0.000000:0.000000
fg:@0.556810:0.302513:0.570686:0.302513:0.570686:0.286152:0.556810:0.286152:0.000000:0.000000
p r:@0.588543:0.293993:0.615042:0.293993:0.615042:0.277632:0.588543:0.277632:0.000000:0.000000:0.000000
q s:@0.588340:0.313439:0.615926:0.313439:0.615926:0.297078:0.588340:0.297078:0.000000:0.000000:0.000000
pr:@0.635828:0.293993:0.650331:0.293993:0.650331:0.277632:0.635828:0.277632:0.000000:0.000000
qs:@0.635257:0.313439:0.650847:0.313439:0.650847:0.297078:0.635257:0.297078:0.000000:0.000000
q:@0.659434:0.302513:0.668703:0.302513:0.668703:0.286152:0.659434:0.286152:0.000000
s:@0.698445:0.302513:0.704821:0.302513:0.704821:0.286152:0.698445:0.286152:0.000000
Producto de números reales por funciones racionales:@0.122489:0.354847:0.540824:0.354847:0.540824:0.337946:0.122489:0.337946:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
():@0.582510:0.355937:0.605711:0.355937:0.605711:0.336003:0.582510:0.336003:0.000000:0.000000
():@0.644179:0.346311:0.667379:0.346311:0.667379:0.326377:0.644179:0.326377:0.000000:0.000000
():@0.643603:0.366860:0.666803:0.366860:0.666803:0.346927:0.643603:0.346927:0.000000:0.000000
():@0.755321:0.355937:0.775905:0.355937:0.775905:0.336003:0.755321:0.336003:0.000000:0.000000
⋅:@0.567327:0.353483:0.571934:0.353483:0.571934:0.337910:0.567327:0.337910:0.000000
=:@0.608366:0.353483:0.618483:0.353483:0.618483:0.337910:0.608366:0.337910:0.000000
∀∈:@0.677838:0.353483:0.715891:0.353483:0.715891:0.337910:0.677838:0.337910:0.000000:0.000000
,:@0.670301:0.352805:0.673508:0.352805:0.673508:0.336416:0.670301:0.336416:0.000000
.:@0.674429:0.352805:0.677635:0.352805:0.677635:0.336416:0.674429:0.336416:0.000000
cf x:@0.557155:0.352805:0.597862:0.352805:0.597862:0.336444:0.557155:0.336444:0.000000:0.000000:0.000000:0.000000
c:@0.621394:0.352805:0.629060:0.352805:0.629060:0.336444:0.621394:0.336444:0.000000
px:@0.633483:0.343179:0.659539:0.343179:0.659539:0.326818:0.633483:0.326818:0.000000:0.000000
qx:@0.633280:0.363731:0.658968:0.363731:0.658968:0.347370:0.633280:0.347370:0.000000:0.000000
x:@0.690866:0.352805:0.698330:0.352805:0.698330:0.336444:0.690866:0.336444:0.000000
Dom f:@0.718876:0.352805:0.766457:0.352805:0.766457:0.336444:0.718876:0.336444:0.000000:0.000000:0.000000:0.000000:0.000000
;  :@0.778674:0.354064:0.789952:0.354064:0.789952:0.337675:0.778674:0.337675:0.000000:0.000000:0.000000
q x:@0.789952:0.354064:0.812820:0.354064:0.812820:0.337702:0.789952:0.337702:0.000000:0.000000:0.000000
( ) ≠:@0.799221:0.354741:0.833109:0.354741:0.833109:0.339168:0.799221:0.339168:0.000000:0.000000:0.000000:0.000000:0.000000
   0:@0.818957:0.354064:0.846138:0.354064:0.846138:0.337675:0.818957:0.337675:0.000000:0.000000:0.000000:0.000000
a) :@0.148449:0.791765:0.167171:0.791765:0.167171:0.774865:0.148449:0.774865:0.000000:0.000000:0.000000
f x:@0.181692:0.791765:0.198738:0.791765:0.198738:0.775404:0.181692:0.775404:0.000000:0.000000:0.000000
( ) +  ( ):@0.186391:0.791765:0.249174:0.791765:0.249174:0.775376:0.186391:0.775376:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g x:@0.222675:0.791765:0.244291:0.791765:0.244291:0.775404:0.222675:0.775404:0.000000:0.000000:0.000000
 :@0.148449:0.918575:0.152263:0.918575:0.152263:0.901675:0.148449:0.901675:0.000000
b) :@0.540917:0.791764:0.560948:0.791764:0.560948:0.774863:0.540917:0.774863:0.000000:0.000000:0.000000
f x:@0.574161:0.791764:0.591206:0.791764:0.591206:0.775403:0.574161:0.775403:0.000000:0.000000:0.000000
( ) –  ( ):@0.578860:0.791764:0.639874:0.791764:0.639874:0.775375:0.578860:0.775375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g x:@0.613375:0.791764:0.634990:0.791764:0.634990:0.775403:0.613375:0.775403:0.000000:0.000000:0.000000
 :@0.540917:0.918574:0.544732:0.918574:0.544732:0.901673:0.540917:0.901673:0.000000
Shutterstock, 151874456.:@0.875231:0.655826:0.875231:0.568000:0.861335:0.568000:0.861335:0.655826:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
():@0.217388:0.831741:0.240589:0.831741:0.240589:0.811808:0.217388:0.811808:0.000000:0.000000
():@0.265503:0.831741:0.288703:0.831741:0.288703:0.811808:0.265503:0.811808:0.000000:0.000000
(:@0.305491:0.842664:0.311627:0.842664:0.311627:0.822730:0.305491:0.822730:0.000000
)(:@0.347119:0.842664:0.360476:0.842664:0.360476:0.822731:0.347119:0.822730:0.000000:0.000000
):@0.395599:0.842664:0.401735:0.842664:0.401735:0.822731:0.395599:0.822731:0.000000
+:@0.242308:0.829287:0.252424:0.829287:0.252424:0.813714:0.242308:0.813714:0.000000
=:@0.291362:0.829287:0.301479:0.829287:0.301479:0.813714:0.291362:0.813714:0.000000
+:@0.349317:0.820767:0.359434:0.820767:0.359434:0.805194:0.349317:0.805194:0.000000
+:@0.372830:0.840213:0.382947:0.840213:0.382947:0.824640:0.372830:0.824640:0.000000
5:@0.361479:0.820090:0.370472:0.820090:0.370472:0.803701:0.361479:0.803701:0.000000
–4:@0.324790:0.839535:0.346239:0.839535:0.346239:0.823146:0.324790:0.823146:0.000000:0.000000
4:@0.385730:0.839535:0.394722:0.839535:0.394722:0.823146:0.385730:0.823146:0.000000
fx:@0.208622:0.828609:0.232780:0.828609:0.232780:0.812248:0.208622:0.812248:0.000000:0.000000
gx:@0.255207:0.828609:0.280895:0.828609:0.280895:0.812248:0.255207:0.812248:0.000000:0.000000
x:@0.338758:0.820090:0.346221:0.820090:0.346221:0.803728:0.338758:0.803728:0.000000
x:@0.313400:0.839533:0.320863:0.839533:0.320863:0.823171:0.313400:0.823171:0.000000
x:@0.362251:0.839533:0.369715:0.839533:0.369715:0.823171:0.362251:0.823171:0.000000
():@0.603017:0.832998:0.626217:0.832998:0.626217:0.813065:0.603017:0.813065:0.000000:0.000000
():@0.651500:0.832998:0.674700:0.832998:0.674700:0.813065:0.651500:0.813065:0.000000:0.000000
(:@0.691488:0.843921:0.697624:0.843921:0.697624:0.823988:0.691488:0.823988:0.000000
)(:@0.733116:0.843921:0.746469:0.843922:0.746469:0.823988:0.733116:0.823988:0.000000:0.000000
):@0.781592:0.843922:0.787729:0.843922:0.787729:0.823988:0.781592:0.823988:0.000000
=:@0.677356:0.830544:0.687472:0.830544:0.687472:0.814971:0.677356:0.814971:0.000000
+:@0.735310:0.822025:0.745427:0.822025:0.745427:0.806452:0.735310:0.806452:0.000000
+:@0.758824:0.841470:0.768941:0.841470:0.768941:0.825897:0.758824:0.825897:0.000000
–:@0.628725:0.829866:0.637939:0.829866:0.637939:0.813478:0.628725:0.813478:0.000000
3:@0.747454:0.821347:0.756447:0.821347:0.756447:0.804958:0.747454:0.804958:0.000000
–4:@0.710765:0.840792:0.732215:0.840792:0.732215:0.824403:0.710765:0.824403:0.000000:0.000000
4:@0.771705:0.840792:0.780698:0.840792:0.780698:0.824403:0.771705:0.824403:0.000000
fx:@0.594228:0.829866:0.618387:0.829866:0.618387:0.813505:0.594228:0.813505:0.000000:0.000000
gx:@0.641182:0.829866:0.666870:0.829866:0.666870:0.813505:0.641182:0.813505:0.000000:0.000000
x:@0.724733:0.821347:0.732196:0.821347:0.732196:0.804986:0.724733:0.804986:0.000000
x:@0.699395:0.840790:0.706858:0.840790:0.706858:0.824429:0.699395:0.824429:0.000000
x:@0.748247:0.840790:0.755710:0.840790:0.755710:0.824429:0.748247:0.824429:0.000000