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# Properties of Functions

A function is that type of relation in which a domain element corresponding to one element exactly in the range set. However, more than one element in domain set can correspond to a single and same element in the range; still the relation is a function.

This can be more easily understood by studying the graphs of the relations.

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## Basic properties of Functions

The first two parameters that are connected with any function are the domain and range. The domain of a function means the set or sets of real values of the variable for which the function is defined. The range is the set or sets of values of the function from a minimum level to maximum level in the domain of the function. Usually these two are expressed in interval notation.

A square bracket is used if the value at that point is included and a round bracket is used when it is not be included. The interval of all real numbers is represented as (-∞,∞).

A function may not be defined before or after certain value of the variable.
For example, the function f(x) = √(1 + x) is not defined for all values of ‘x’ before -1 and the function f(x) = √(1 - x) is not defined for all values of ‘x’ after 1. But in many cases a function may not be defined only for a particular or for some values of the variable.

At such places the function is said to be have discontinuities.