# Ensayo matematicas iii

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ENSAYO MATEMATICAS III

JORGE LUIS JIMENEZ MORA

COD 2007252134

ESCUELA COLOMBIANA DE CARRERAS INDUSTRIALES ECCI

BOGOTA 30 DE AGOSTO DE 2010>

Domain

The domain of a function is the complete set of possible values of the independent variable in the function.
In plain English, this definition means:
The domain of a function is the set of all possible x valueswhich will make the function "work" and will output real y-values.
When finding the domain, remember:
• The denominator (bottom) of a fraction cannot be zero
• The values under a square root sign must be positive
Example: The function y = √(x + 4) has the following graph.
[pic]
The domain of the function is x ≥ −4, since x cannot take values less than −4. (Try some values in yourcalculator, some less than −4 and some more than −4. The only ones that "work" and give us an answer are the ones greater than or equal to −4).

Note:
1. The enclosed (colored-in) circle on the point (-4, 0). This indicates that the domain "starts" at this point.
2. That x can take any positive value in this example.

Range

The range of a function is the complete set of all possibleresulting values of the dependent variable of a function, after we have substituted the values in the domain.
In plain English, the definition means:
The range of a function is the possible y values of a function that result when we substitute all the possible x-values into the function.
When finding the range, remember:
• Substitute different x-values into the expression for y to see what ishappening
• Make sure you look for minimum and maximum values of y

Example 1: Let's return to the example above, y = √(x + 4). We notice that there are only positive y-values. There is no value of x that we can find such that we will get a negative value of y. We say that the range for this function is y ≥ 0.
[pic]
Example 2: The curve of y = sin x shows the range to be betweeen −1 and 1.[pic]
The domain of the function y = sin x is "all values of x", since there are no restrictions on the values for x.

More Domain and Range Examples
You can see more examples of domain and range in the section Inverse Trigonometric Functions.
Note 1: Because we are assuming that only real numbers are to be used in the domain and range of a function, values that lead to division by zero orto imaginary numbers are not included. The Complex Numbers chapter explains more about imaginary numbers.
Note 2: Many people ask for the square root example, "What about the negative values when we find a square root?" A square root has at most one value, not 2. See this discussion: Square Root 16 - how many answers?
Also, we are talking about the domain and range of functions, which have atmost one y-value for each x-value.

ENSAYO DOMINIO Y RANGO DE UNA FUNCION

El dominio de una función es el conjunto completo de valores posibles de la variable independiente en la función.
En la llanura Inglés, que significa esta definición:
El dominio de una función es el conjunto de todos los valores posibles x lo que hará la función de "trabajo" y la producción real y los valores.
Alencontrar el dominio, recuerde:
• El denominador (abajo) de una fracción que no puede ser cero
• Los valores bajo un signo de raíz cuadrada debe ser positivo
Ejemplo: La función y = √ (x + 4) tiene el siguiente gráfico.
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