Question: For each relation, decide whether or not it is a function. | Relation 1 | Relation 2 |…

For each relation, decide whether or not it is a function.

Relation 1	Relation 2
Domain	Range
$s$	$u$
$z$	$n$
$n$	$v$
$w$	$n$
$-9$	rock

| Function | Not a function | Function | Not a function |

Relation 3	Relation 4
$\{(-6, -6), (2, 2), (4, -2), (-2, -2)\}$	$\{(u, 1), (x, 5), (x, -8), (x, -2)\}$
Function	Not a function

Solution

To determine if each relation is a function, we check if every element in the domain is mapped to exactly one element in the range. Relation 1: - Domain: \( s, z, n, w \) - Range: \( u, n, v, n \) Each domain element is mapped to exactly one range element. - Conclusion: Function Relation 2: - Domain: \( -3, -9, -5, -7, -9 \) - Range: \( \text{chair, tree, door, star, rock} \) The domain element \(-9\) maps to two different range elements: tree and rock. - Conclusion: Not a function Relation 3: \[ \{(-6, -6), (2, 2), (4, -2), (-2, -2)\} \] Each domain element is unique and each maps to one range element. - Conclusion: Function Relation 4: \[ \{(u, 1), (x, 5), (x, -8), (x, -2)\} \] The domain element \(x\) maps to multiple range elements: 5, -8, and -2. - Conclusion: Not a function