# Basic Understanding of Domain and Range # Basic Understanding of Domain and Range and its Principles

This article provides an insight into what domain and range are and the process to calculate the two quantities. But before moving on, we should check what exactly a function is. Using mathematics, we can easily associate a function to a device which produces some output in relation to a given input. We can generally illustrate it using the example of a food packaging machine. When we put food into the food packaging machine, the food gets introduced and results in a packaged condition. Thus, in this illustration, the food can be considered as domain and the output or the packaged food is considered the range. Here the food packaging machine is the function and is similar to the food packaging machine which packs a single food each time, a function also produces a single output each time.

## Evolution of Function

The concept of function was first introduced by Rene Descartes, a French Philosopher and mathematician, belonging to the early seventeenth century. In his book, Geometry he used this idea to find solutions for mathematical problems. After around fifty years, Gottfried Wilhelm Leibniz modeled the term function after the publication of the book. Later it was Leonhard Euler who came up with the equation y = f(x) which represents a function.

## Real Life Scenarios of a Function

In terms of mathematics, function has proved to be very essential. In fact, there are some real life scenarios which can represent a function. The following have been enlisted below. • Finding the circumference of a circle: The circumference of a circle can be considered as a function of its radius or diameter. The equation looks like: C(d) = dπ (where d is the diameter) or C(r) = 2πr.
• Getting the shadow of an object: The magnitude or length of a shadow depends on the height of an object.
• The location of a moving object: The placement or position of a moving object like a cycle is a function related to time.
• Weight of a person: The weight of a person depends on many points such as age and height. This can also be related to a function.

## Defining Domain and Range of a Function

The domain of a function is basically the numbers that are used as inputs, when inserted into a function, results in a defined value. Generally, we can define the domain of a function as the possible values of ‘x’ to make the equation true. Other restrictions of a function represent when an equation is divided by zero or the square root of a negative number. Thus, the equation f(x) = x2 can be termed as a valid function since any value of x can provide us with a defined answer. Hence, we can state that the domain of a function is always a real number.

The range of a function can be defined as the set of answers of an equation for a given set of inputs. Mathematically, the range is the output or the y value found in a function. Only one range of a given function exists.

## Specifying Domain and Range using Intervals

So, it is better to get an idea of interval notations, since domain and range are basically used within interval notations. Below are the interval notations used to utilize domain and range. They are as follows.

1.     First, we need to jot down the numbers in ascending order and separating those using commas.
2.     We should use parentheses or round brackets, (), to enclose a number that determines that the end points are not included.
3.     Similarly, we should use square brackets or [] for enclosing a number to determine that the end points are included within.

This is the basic concept of domain and range. For more ideas and concepts, visit website of Cuemath available online.

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