DOMAIN AND RANGE OF FUNCTIONS

How to find the domain and range of a relation given by a set of ordered pairs ?

Domain is nothing but the values of "x" for which the given function is defined. 

Range is nothing but the values of "y" that we get for the the given domain (values of "x"). 

Example :

Which of the following relations are functions from

A = { 1, 4, 9, 16 } to B = { –1, 2, –3, –4, 5, 6 }

In case of a function, write down its domain and range.

f₁ = { (1, –1), (4, 2), (9, –3), (16, –4) }

Solution :

From the set of ordered pairs, the list of first elements are domain and second elements are range.

Domain  =  {1, 4, 9, 16}

Range  =  {-1, 2, -3, -4}

Co domain  =  { –1, 2, –3, –4, 5, 6 }

To see more examples, please click on the link.

How to find the domain and range from a relation

How to find domain and range of a mapping diagram ?

Example : 

Let A  =  {1, 2, 3} and B  =  {5, 6, 7, 8}. 

f is the function which maps the elements from A to B as shown below. 

Find, the domain, co-domain and range of f. 

Solution :

Domain (f)  =  A  =  {1, 2, 3}

Co-domain (f)  =  B  =  {5, 6, 7, 8}

Range (f)  =  {5, 6, 7} 

To get more example,

Domain codomain and range of a function

How to find domain and range of a mapping diagram

Domain and Range from Graph

Domain :

The domain is the set of possible input values, which are shown horizontally on the x-axis.

Range :

The range is the set of possible output values, which are shown vertically on the y-axis.

Example :

Solution :

Finding the domain :

In the given graph, the possible values of x are -4, -3, -2 ……… there are spread horizontally on the x-axis.

Because the graph starts at -4 on the x-axis.

So, the domain (x) is x > -4

Finding the range :

In the given graph, the possible values of y are -2, -1, 0 ……… there are spread vertically on the y-axis.

Because the graph starts at -2 on the y-axis.

So, the range (y) is y > -2

To see more examples,

find domain and range from a graph

Domain and Range of Polynomial Function

Example :

Find the domain of the following function

f(x)  =  1 / (x + 2)

Solution :

The given function accepts all real values except -2. In the given function if we apply -2 instead of x, it will become undefined.

Hence the domain of f(x) is R - {-2}

To see more examples.

Domain of a function worksheet

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