[b]Te invito a trabajar el tema de las funciones, y de manera específica la función lineal:[/b][br][br]Recuerda que en esta sección repasamos los conceptos de función, dominio, codominio, imagen, anti-imagen y gráfica; ademas de que resolveremos uno que otro ejercicio:[br][br][b]FUNCIÓN[/b][br][br]Definición:[br][br]Sean A y B conjuntos no vacíos. Una función de A en B es una relación que asigna a cada elemento x del conjunto A uno y solo un elemento y del conjunto B.[br][br]Se expresa como: f: A  [img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAICAYAAAD0g6+qAAAAbUlEQVQoFWP4TyXAQI45l54e/X/ywS4UrQzrL874P+VQKUm4aXvc/8pNwSiGMRSsdf9/+9VFkvG3X5//LzvTAzeMbINA/gJ5D2QYCDDMPd5IkrdAwQDyGoiGGQI2CGwcicSB2+tQDCHbIGz2AgDA7wRaxvltzgAAAABJRU5ErkJggg==[/img] B[br][br]X [img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAICAYAAAD0g6+qAAAAbUlEQVQoFWP4TyXAQI45l54e/X/ywS4UrQzrL874P+VQKUm4aXvc/8pNwSiGMRSsdf9/+9VFkvG3X5//LzvTAzeMbINA/gJ5D2QYCDDMPd5IkrdAwQDyGoiGGQI2CGwcicSB2+tQDCHbIGz2AgDA7wRaxvltzgAAAABJRU5ErkJggg==[/img] f(x) = y[br][br][br][img]data:image/png;base64,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[/img][br][br][br][br][b]Dominio:[/b] es el conjunto de todos los valores para los cuales está definida la función y se denota Dom f.[br][br][b]Rango:[/b] es el conjunto de todos los valores que toma la variable dependiente (Y), y se denota Ran f.[br][br][b]Imagen[/b] es el valor que toma la variable  y respecto a un valor determinado de la variable  x.[br][br][b]La antiimagen[/b] es el valor que toma la variable  x respecto a un valor que ha tomado la variable  y.[br][br][b]Función Creciente:[/b] es aquella que al aumentar la variable independiente, también aumenta la variable dependiente.[br][br][b]Función Decreciente: [/b]es aquella que al aumentar la variable independiente, la variable dependiente disminuye.[br][br][b]Rango o Recorrido de f:[/b][br][br]Es aquel subconjunto del codominio en el cual todos sus elementos son imagen de alguna preimagen del dominio o conjunto de partida. Se denota por R(f).[br][br][b]La función lineal [br][br][/b]Una [b]función lineal[/b] es una [b]función[/b] cuyo dominio son todos los números reales, cuyo codominio son también todos los números reales, y cuya expresión analítica es un polinomio de primer grado.[br]

[br]Si el coste de fabricación de un bolígrafo es de 0,3$ por unidad y se venden por 0,5$, calcular:[br][br][list=1][*]La función de beneficios en función del número de bolígrafos vendidos. Representar su gráfica.[/*][*]Calcular los beneficios si se venden 5.000 bolígrafos.[/*][*]Calcular cuántos bolígrafos deben venderse para generar unos beneficios de 1.648$.[/*][/list][b]Apartado [i]a[/i]:[br][br][/b]Como cada bolígrafo se vende por 0,5$ y su coste de fabricación es de 0,3$, los beneficios por cada bolígrafo vendido son[br][br][img]https://www.matesfacil.com/ESO/funciones/BP1-1.png[/img][br][br]Por tanto, si se venden x bolígrafos, los beneficios son[br][br][img]https://www.matesfacil.com/ESO/funciones/BP1-2.png[/img][br][br]La función de beneficios es[br][br][br][img]https://www.matesfacil.com/ESO/funciones/BP1-3.png[/img][br][br]Exigimos x sea mayor o igual que 0 ( x ≥ 0x ≥ 0 ) porque el número de bolígrafos vendidos no puede ser negativo.Para representar la gráfica, damos algunos valores a xx para obtener algunos puntos:[br][br][br][img]https://www.matesfacil.com/ESO/funciones/BP1-4.png[/img][br][br]y la grafica de la función es:[br][br][img]data:image/png;base64,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[/img][br][br][b]Apartado [i]b[/i]:[br][br][/b]Si se venden 5.000 bolígrafos, aplicando la función, los beneficios son[br][br][br][img]https://www.matesfacil.com/ESO/funciones/BP1-5.png[/img][br][br]Los beneficios son 1.000$.[br][br][b]Apartado [i]c[/i]:[br][br][/b]Queremos calcular el número xx de bolígrafos vendidos para que las ganancias sean 1.648$. [br][br]Para ello, resolvemos la ecuación[br][br][br][img]https://www.matesfacil.com/ESO/funciones/BP1-6.png[/img][br][br]Es decir,[br][br][br][img]https://www.matesfacil.com/ESO/funciones/BP1-7.png[/img][br][br][br]Deben venderse 8.240 bolígrafos.[br][br][br]

Resolvamos el siguiente ejercicio:[br][br][b]1.[/b] Un algodonero recoge 30 Kg cada hora, y demora media hora preparándose todos los días cuando inicia la jornada. La función lineal que representa esta situación es [i]y = 30x – 15[/i] donde [i][b]y [/b][/i]representa los Kg de algodón recogido y [i][b]x [/b][/i]el tiempo transcurrido en horas.[br][br]Realiza una tabla para la anterior función y grafícala.[br]¿Cuántos Kg de algodón se recogerán en una jornada de 8 horas?[br][br][b]Solución:[br][br][/b]Primero realizamos la tabla.[br][br][br][right][/right] [br] [br] [table][br] [tr][br] [td][b][/b][center][b]Y[/b][br] [b](Kg[br] algodón)[/b][/center][b] [/b][br] [center][b][/b][/center][center][/center][center][b][/b][/center][/td][td][b][/b][b][/b][center][b]X[/b][br] [b](Tiempo[br] en horas)[/b] [/center][center][/center] [center] [b] [/b][/center][br] [/td][br] [/tr][br] [tr][br] [td][br] 0.5[br] [/td][br] [td][br] 0[br] [/td][br] [/tr][br] [tr][br] [td][br] 1[br] [/td][br] [td][br] 15[br] [/td][br] [/tr][br] [tr][br] [td][br] 1.5[br] [/td][br] [td][br] 30[br] [/td][br] [/tr][br] [tr][br] [td][br] 2[br] [/td][br] [td][br] 45[br] [/td][br] [/tr][br][/table][br][br][br]y luego graficamos:[br]

Ahora para saber cuanto algodón se recoge en 8 horas:[br][br][i]y = 30x – 15    [/i]para [i]x = 8[/i] necesitamos hallar el valor de [i]y [/i]para eso remplazamos a la [i]x [/i]por su valor que es [i]8 [/i]y nos queda[br][br][br][i]y = 30(8) – 15 = 240 - 15 = 225 [/i][b]  [/b] (recuerda que 3[i]0(8)[/i] es un producto)[br][i][b]y = 225 [/b][/i][b]Kg[br][br][/b]La cantidad de algodón recogido en ocho horas es de [b]225 kg[/b]

Si tienes problemas para realizar la tabla repasa los vídeos [math]\downarrow[/math] :