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3.1. Todo tiene que funcionar

 

Glosario

Argumento

Persona hablando en televisión

Definición:

Razonamiento que se usa para convencer o demostrar que algo es verdad.

Ejemplo:

En la noticia se dan datos que apoyan el argumento.

Variable

Matemáticas

Definición:

En  funciones, una variable es cada uno de los conjuntos que intervienen en la relación.

Al primero se le llama variable independiente (x) y al segundo variable dependiente (y).

Si se hace una descripción verbal, el segundo (y) se lee antes que el primero (x).

Ejemplo:

En la función que relaciona el precio de un alimento con su peso, precio y peso son las variables.

El precio es la variable dependiente (la segunda, "y") y el peso la independiente (la primera, "x").

Comprobando si algo funciona… ¡o no funciona!

Mujer leyendo el periódico

En la redacción del periódico, no todo funciona siempre a la primera. Ya sabes interpretar una gráfica, pero es importante que comprendas el concepto de función y cómo relacionan variables. Aprenderás a diferenciar entre las variables que mandan (independientes) y las que obedecen (las dependientes).

Recuerda que, para ejercer un buen periodismo, debes comprobar siempre si algo funciona… ¡o no funciona!

Predicción del tiempo que funciona

Ya está casi lista la predicción del tiempo. Sólo falta ilustrar la noticia con la gráfica apropiada pero... ¿cuál es?

Viernes 7 de marzo
El Mathington Post

EL TIEMPO

Sábado 8 de marzo


A lo largo del día las temperaturas oscilarán entre los 7 °C y los 17 °C. Nos espera una mañana fría, propia de esta época del año, con temperaturas por debajo de los 8 °C, a la que seguirá una tarde fresca en la

que se alcanzan los 16 °C a las 14 h y los 17 °C a las 15 h. A partir de las 16 h las temperaturas comenzarán su descenso y, a partir de las 23 h, se situarán por debajo de los 10 °C.
Interrogación
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Lo que funciona...

Gráficas

Gráfica con una predicción del tiempo

- ¿Qué temperatura va a hacer mañana? Depende. No hace siempre la misma temperatura. Es variable. Decimos que la variable "Temperatura" es una variable dependiente. 

- ¿Y de qué depende? Del momento del día. También es algo variable. Decimos que la variable "Hora" es una variable independiente.

Pero, si la gráfica está bien construida, si la gráfica "funciona", debe hacer corresponder a cada momento del día una única temperatura.

Ejemplos:

A las 2 h la temperatura era de ºC.

A las 12 h la temperatura era de ºC.

Observa que el eje horizontal escribimos las horas (variable independiente) y en el eje vertical la temperatura (variable dependiente).

La variable "Hora" toma valores entre y 24.

La variable "Temperatura" toma valores entre 7 y .

Tablas

En la cafetería del instituto tienen esta tabla para que quienes trabajan allí puedan calcular rápidamente cuánto tienen que cobrar en cada mesa:

CAFÉS PEQUEÑOS
Nº unidades Coste 
1 1,60 €
2 3,20 €
3 4,80 €
4 6,40 €

- ¿Cuánto le costaron los cafés? Depende. Decimos que la variable "Coste de los cafés" es una variable .

- ¿De qué depende? Del número de cafés que haya tomado. Decimos que la variable "Número de cafés" es una variable

Si los precios están bien puestos, a cada cantidad de cafés le debería corresponder un único precio.

Ejemplos: 

Si hemos tomado cinco cafés, tendremos que pagar €.

Si en una mesa han tomado seis cafés, tendrán que pagar €.

Fórmulas

Perímetro de un cuadrado = 4 · lado

- ¿Cuánto mide el perímetro de un cuadrado? Depende. Decimos que la variable "Perímetro del cuadrado"  es una variable .

- ¿Y de qué depende? De lo que midan los lados. Decimos que la variable "Lado del cuadrado" es una variable .

Si hacemos los cálculos bien, para cada lado del cuadrado obtendremos un único perímetro.

Ejemplos:

Si tenemos un cuadrado que mide 2 cm de lado, su perímetro es cm.

Si tenemos un cuadrado que mide 7cm de lado, su perímetro es cm.

Textos

A Marcos le pagan 15 € por cada hora que trabaja.

- ¿Cuánto le pagan a Marcos?  Depende. Decimos que la variable "Dinero que cobra Marcos" es una variable .

- ¿Y de qué depende? De las horas que trabaje. Decimos que la  variable "Horas que trabaja Marcos" es una variable .

Si el texto "funciona" y nos dicen cuántas horas ha trabajado Marcos, deberíamos saber, sin lugar a dudas, cuánto le van a pagar a Marcos.

Ejemplos:

Si Marcos trabaja 3 horas le pagarán €.

Si Marcos trabaja 4 horas le pagarán €.

Habilitar JavaScript

...es una función

Función

 Una función es una regla que asigna a cada número de un conjunto un único número de otro conjunto

Representación de una función como una máquina que transforma los números que entran en otros que salen.

Por ejemplo, asignar en un videojuego tres puntos por cada avión que derribes, es una función.

1 avión derribado → 3 puntos

2 aviones derribados → 6 puntos

3 aviones derribados → 9 puntos

...

Formas de expresar una función

Gráfica1. Funciones expresadas mediante gráficas

Una gráfica representa a una función si, observando sus puntos, para cada valor de x hay un único valor de y.

En los puntos (x,y), el primer número también se llama abscisa y el segundo se llama ordenada.

El motivo es que, los ejes X e Y se llaman eje de abscisas y eje de ordenadas, respectivamente.

Tabla2. Funciones expresadas mediante tablas

Una función viene expresada por una tabla si a cada número de la primera columna le corresponde un único número de la segunda.

Fórmula3. Funciones expresadas mediante fórmulas

Una función viene expresada por una fórmula si al sustituir x en esa expresión, obtenemos un único resultado. Este se representa por f(x) o por y.

Como debe cumplirse que para cada x haya una sola y, puede haber fórmulas que no representan una función.

Texto4. Funciones expresadas mediante texto

Una función viene expresada por un texto si en él se describe una relación entre dos conjuntos que cumpla las condiciones de la definición.

Variable

Una variable es cada uno de los conjuntos que se relacionan en la función.

La variable dependiente (y), es la que calculamos a partir de la otra variable (x), a la que llamaremos variable independiente.

Cuando se da una relación entre dos variables en un texto, habitualmente se escribe antes la dependiente.

Gráfica del crecimiento de un bebé

Obsérvalo en este ejemplo:

En la siguiente gráfica se refleja el crecimiento de un bebé en centímetros, durante los 24 primeros meses de vida.

A medida que el bebé cumple meses, su altura va cambiando.

La variable "Altura" es la variable dependiente (siempre representamos la variable dependiente en el eje vertical, o eje de ordenadas).

La variable "Edad" es la variable independiente (siempre representamos la variable independiente en el eje horizontal, o eje de abscisas).

Dominio

El dominio de una función es el conjunto de valores que puede tomar la variable independiente

En el ejemplo del crecimiento del bebé, la variable "Edad" toma valores de 0 a 24.

Recorrido o imagen

El recorrido de una función es el conjunto de valores que puede tomar la variable dependiente

En el ejemplo del crecimiento del bebé, la variable "Altura" toma valores de 50 a 90.

Argumentando si funciona o no una gráfica

Para ejercer un periodismo de calidad tienes que argumentar tus respuestas. Por eso, cuando aceptes o descartes una gráfica, debes justificar tu decisión.

Puede haber uno o más argumentos que apoyen tus ideas y debes señalarlos todos.

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Su navegador no es compatible con esta herramienta.

Una cuestión de estilo

En un periódico se debe cuidar la escritura y mantener una notación precisa y estándar.

Por ejemplo, si tenemos una función que asigne a cada número su doble más 3, y hemos decidido llamarle fescribiremos y = 2x + 3 o bien f(x) = 2x + 3

En vez de escribir "El valor que le asigna la función al número 5 es 2 · 5 + 3 =13", escribiremos f(5) = 2 · 5 + 3=13

Vamos a practicar un poco.

Ejercicio de estilo 1

María tiene 15 euros ahorrados y va a ahorrar 2 euros más cada semana.

El dinero que tendrá María es igual a 15 euros más 2 euros por cada semana que pase → y = 15 + 2x o también f(x) = 15 + 2x

El dinero que tendrá María dentro de 2 semanas→ f(2) = 15 + 2 · 2 = 19

El dinero que tendrá María dentro de 7 semanas→ f( ) = 15 + 2 · =

El dinero que tendrá María dentro de 10 semanas→ f( ) = + 2 · =

El dinero que tendrá María dentro de semanas→ f( ) = + 2 · 20=

Ejercicio de estilo 2

En el restaurante tienen almacenados 300 litros de aceite, pero se prevé un gasto de 15 litros diarios.

El aceite que quedará en el almacén es igual a 300 litros menos 15 por cada día que pase → y = 300 - 15x o también f(x) = 300 - 15x

El aceite que quedará en el almacén dentro de 2 días →  f( ) = 300 - 15 · =

El aceite que quedará en el almacén dentro de 5 días →  f( ) = - 15 · =

El aceite que quedará en el almacén dentro de una semana →  f( ) = - 15 · =

El aceite que quedará en el almacén dentro de días →  f( ) = - 15 ·15 =

Ejercicio de estilo 3

Gráfica

f(-4) =

f(-3) =

f(-2) =

f(0) =

f(1) =

f(2) =

f(4) =

Ejercicio de estilo 4

Gráfica roja

g(-3) =

g(-2) =

g(1) =

g(4) =

g(6) =

g(8) =

g(10) =    

g(12) =

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