Chapter 1, Problem 1GYR

To determine

Define Function, domain, range, and arrow diagram for the function

Explanation of Solution

Function:

A function is expressed in terms of dependent and independent variable. For every function, the value of one variable quantity changes according to another variable quantity, that is both the variables depends on each other. If x and y are considered as a two variables, it is expressed as follows:

$y=f\left(x\right)$

Here, f is function, x is independent variable (input value of f), and y is dependent variable (output value of f at x).

The definition of Function as follows:

The function is defined as. “A function f from a set D to a set Y is a rule that consigns a unique value $f\left(x\right)$ in Y to each x in D”.

Domain:

The possibility of all input values of the function is called domain of the function. The all input values of set D is domain of the function.

Range:

The variable x varies throughout the set D and provide the set of all output value of $f\left(x\right)$ is called range. The range may not take in to account in every element in the set Y.

Arrow diagram:

Function can represented by an arrow diagram.

Draw the arrow diagram as shown in Figure 1.

Refer to Figure 1.

• Every arrow connects to an element of the domain D a single element in the set Y.
• The function $f\left(a\right)$ connects with a and the function $f\left(x\right)$ connects with x. The functions has the similar output value for two varies elements in the domain but single output value $f\left(x\right)$ obtained from each input element x.