Question

What is domain ,range and function with examples?

Answer 1

The domain of a function f ( x ) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.Example 1:
Consider the relation { ( 0 , 7 ) , ( 0 , 8 ) , ( 1 ,7 ) , ( 1 , 8 ) , ( 1 , 9 ) , ( 2 , 10 ) } .
Here, the relation is given as a set of ordered pairs. The domain is the set of x -coordinates, { 0 , 1 , 2 } , and the range is the set of y -coordinates, { 7 , 8 , 9 , 10 } . Note that the domain elements 1 and 2 are associated with more than one range elements, so this is not a function.

Answer 2

Answer:

Domain : It is defined as a set of all points for which the function is real and defined.

Range : It is defined as a set of all values of dependent variable for which the function is defined.

Consider the function as example : f(x) = -(x + 3)(x - 1)

Now, The given function f(x) is a polynomial function and is real and defined for all the real numbers. So, The domain of the given function f(x) is given by :

Domain : All real numbers

Now, To find range of the function :

As seen from the graph, the maximum value of the function is at (-1,4)

So, The range consists of all the values less than or equal to 4

⇒ Range : All real numbers less than or equal to 4