Ejercicio 22. Análisis de patrones numéricos para construir polinomios.

Introducción.
La función potencia [img]https://s0.wp.com/latex.php?latex=f+%3AR%5Clongrightarrow+R&bg=ffffff&fg=333333&s=0[/img]es una función de la forma  [img]https://s0.wp.com/latex.php?latex=f%28x%29%3Dax%5En&bg=ffffff&fg=333333&s=0[/img] donde a es un número real, distinto de 0, y n es un número natural distinto de 1. La función potencia esta definida para los números reales y su gráfica depende del exponente.[br]Ocupando el Applet de arriba (pincha en la imagen) responde las preguntas a continuación.[br][br][b]Actividad 1:[br][/b]1.- Observa la gráfica de [img]data:image/png;base64,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[/img][br][br]A medida que el exponente aumenta, ¿Qué sucede con las gráficas de las funciones?[br][br]2.- Observa la gráfica de [img]data:image/png;base64,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[/img][br][br]A medida que el exponente aumenta, ¿Qué sucede con las gráficas de las funciones?[br][br]3.- ¿Qué puedes concluir de la actividad anterior? Anota la conclusión en tu cuaderno.[br][br]4.-Observa la gráfica de [img]data:image/png;base64,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[/img][br][br]A medida que el coeficiente aumenta, ¿Qué sucede con las gráficas de las funciones?[br][br]5.-Observa la gráfica de 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Information: Ejercicio 22. Análisis de patrones numéricos para construir polinomios.