# So what is Domain and Range? Let's check it out

In this lesson , students will be able to know domain and range definition with examples

**Introduction**

A rule of association between input and output values is referred to as a mathematical ‘function’. Functions or relations link between independent variables or input values , which can be manipulated by situations , and dependent variables or output values.

The couple of terms i.e. domain and range are important components of a function. So let’s define domain and range.

## What is domain and range?

**Domain**

The set of all potential independent values at which a function is defined is called domain of that function.

**Range **

The set of potential dependent values produced by a function from the domain values is known as range of that function.

**Problem 1 **

## Find domain and range of function shown in the diagram

**Solution**

Let’s say the given function f.

Domain of f will be the set { A, B , C , E} where D is not included because the given function is not defined at this domain.

Range of f will be the set { 1, 2 , 3 , 4} where 5 is excluded because there is no domain value for it.

**Problem 2 **

## Find domain and range of f (x) = x

**Solution**

As x can be any natural number . So ,

Domain: { 1, 2 , 3 , … }

Range : { 1 , 4 , 9 ,… }

**Problem 3 **

**What is domain and range for **

**Solution**

To find the domain of the given function , we must first consider that values for which the function will be undefined. In this case , there is none of such values except 1 that can undefine the function.

For all values of domain , the range can be any real number except zero.

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