Question

How do you find the domain and range of the relation, and state whether or not the relation is a function \left\\{ {\left( { - 3,2} \right),\left( {0,3} \right),\left( {1,4} \right),\left( {1, - 6} \right),\left( {6,4} \right)} \right\\}?

Answer 1

In the given question, we have been given a relation. We have to find the domain and the range of the relation. Also, we have to check whether the given relation is a function or not. For the first part, the domain is the left side of the ordered pair while range is the right side. Then, we check for if it is a function by seeing if one value of domain has multiple ranges, and if it does, then it is not a function.

Complete step by step answer:
The given relation is:
\left\\{ {\left( { - 3,2} \right),\left( {0,3} \right),\left( {1,4} \right),\left( {1, - 6} \right),\left( {6,4} \right)} \right\\}
For calculating the domain – the abscissa of the ordered pairs.
Hence, domain is – $\left( { - 3,0,1,6} \right)$
For calculating the range – the ordinate of the ordered pairs.
Hence, the range is – $\left( {2,3,4, - 6} \right)$
Now, this relation is clearly not a function because if it were a function, then a domain has a unique range. But here, the domain $1$ has two values of range – $4$ and $- 6$.

Note: In the given question, we had to find the domain and range of a relation. Then we had to check if the given relation is a function. That was done by seeing if one value of domain has multiple ranges, and if it does, then it is not a function. And here, the domain $1$ had two ranges – $4$ and $- 6$, and hence, this relation was not a function. We do not write repeated values.