Question

What is the domain and the range of \[\left\{ \left( 2,-3 \right),\left( 4,6 \right),\left( 3,-1 \right),\left( 6,6 \right),\left( 2,3 \right) \right\}\]?

Answer 1

Hint: In this given question, we have been given a relation. We have to find the domain and the range of a function. For finding the domain, the domain is the left side of the ordered pair while range is the right side of the ordered pair.

Complete step by step solution:
Domain is defined as the set of the first number in every pair (those are the x-coordinates or the abscissa).
Range is defined as the set of the second number of all the pairs (those are the y-coordinates or the ordinates).
In other words, domain and range is defined as
Domain of a function \[y=f\left( x \right)\]is a set of all those values for which function is defined. So, domain contains all possible values of x for which y exists.
Range of a function contains all the possible values of y for which x exists.
Above two definitions about Domain and Range are not used to our problem, it is just a reference.
Let us solve the given question:
The given relation is
\[\left\{ \left( 2,-3 \right),\left( 4,6 \right),\left( 3,-1 \right),\left( 6,6 \right),\left( 2,3 \right) \right\}\]
 The abscissa of above relation is \[\left( 2,3,4,6 \right)\]
 The ordinates of above relation is \[\left( -3,-1,3,6 \right)\]
For calculating the domain- the abscissa of the ordered pairs.
Hence, domain is \[\left( 2,3,4,6 \right)\]
For calculating the domain- the ordinates of the ordered pairs.
Hence, range is \[\left( -3,-1,3,6 \right)\].

Note: Whenever we face such questions the key concept is to be clear about the definitions of domain and range. Do not make the mistake of writing the closed brackets for range and domain here, keep in mind.