91Ó°ÊÓ

The given functions are,

F $\left\{(-3,2),(4,1),(-3,5)\right\}$

G$\left\{(2,-1),(4,-1),(2,6)\right\}$

H $\left\{(-3,-4),(-3,6),(8,-2)\right\}$

J$\left\{(5,-1),(3,-2),(-2,-2)\right\}$

Which of the given relation is a function.

A relation is called a function if the following conditions are satisfied:

1) Every value in its domain has a unique value in its codomain.

2) For every value of $x$, there is a unique value of $y$.

3) For every value of $x$, there must be only one value of $y$.

Considering the relation F. F is $\left\{\left(−3,\text{ }2\right)\text{ }\left(4,\text{ }1\right)\text{ }\left(−3,\text{ }5\right)\right\}$.

The element $-3$of domain is paired with 2 and 5 of range. So, F is not a function.

Considering the relation G. G is $\left\{\left(2,\text{ }−1\right)\text{ }\left(4,\text{ }−1\right)\text{ }\left(2,\text{ }6\right)\right\}$.

The element 2 of domain is paired with $-1$and 6 of range. So, G is not a function

Considering the relation H. H is $\left\{\left(−3,\text{ }−4\right)\text{ }\left(−3,\text{ }6\right)\text{ }\left(8,\text{ }−2\right)\right\}$.

The element $-3$of domain is paired with$-4$ and 6 of range. So, H is not a function.

Considering the relation J. J is $\left\{\left(5,\text{ }−1\right)\text{ }\left(3,\text{ }−2\right)\text{ }\left(−2,\text{ }−2\right)\right\}$.

One element of the domain is paired with only one element of the range. So, J is a function.

Hence, the correct option is (J).