# Domain vs. Range

**Difference Between Domain and Range**

What is a mathematical function? In simple terms, it is a relationship between two sets of variables one of which is independent while the other is dependent. The one which is dependent is known as the Domain, while the other which is dependent is called Range. In a simpler manner, for two dimensional Cartesian coordinate system or XY procedure, the variable along the x-axis is known as Domain whereas the variable along the y-axis is called the Range.

Considering a simple relation, mathematically, {(2, 3), (1, 3), (4, 3)}. In this example, Domain is {2, 1, 4}, while the Range is {3}.

A Domain is a set of all possible input values in any relation, which essential means the output value in a mathematical function relies upon each member of the Domain. The Domain value differs in various mathematical problems and relies on the function for which it is solved. In case we mention about cosine, then domain is the set of all possible real numbers either higher than the 0 value or below the 0 value, it could also be 0.

The domain value could not be less than 0 for the square root, it should actually be minimum 0 or higher than 0. It could be said in other words that the domain of square root is always 0 or a positive value. For complicated and real equations, the domain value is a subset of complex or real vector space. If we would like to solve a partially differential equation for looking for the value of domain, then the response should lie within three dimensional space of Euclidean geometry.

Taking an example, If y=1/1-x, then its domain value is calculated as 1-x=0 And x= 1, therefore its domain could be set of all real numbers except 1.

A Range is the set of all possible output values in a mathematical function. The Range values are also known as dependent values since these values could only be calculated by putting the domain value in the function. Simply said, it can be considered that if domain value of a function y=f(x) is x, then its range value will be y. Taking an example, if Y=1/1-x, then its range value will be a set of real numbers, since the values of y for every x are once again real numbers.

In comparison, the domain value is an independent variable, while range value depends upon domain value, so it is dependent variable. The domain is a set of all input values while on the other hand; range is a set of those output values that a function produces by entering the value of domain. Here is a better theoretical example to comprehend the variance between domain and range. Take into consideration the hours of sunlight during whole day. The domain is the number of hours between sunrise and sun set. While the value of range is between 0 to maximum elevation of sun and to consider this example, you need to bear in mind the hours of daylight, which differ according to season meaning either winter or summer. There is another thing to pay attention which is latitude. You should calculate the domain and the range for specific latitudes.

While there is hardly any doubt, both the domain and range are mathematical variables and correlate with each other since value of range depends upon the value of domain. However, both variables have different attributes and individual individuality in any one mathematical function.