Question

is the relation a function? select the best answer. {(2, -4), (-2, 4), (2, 5), (5, -1), (-1, 5)} no, the relation is not a function. the domain values of -1 and 2 are both assigned to 5. yes, the relation is a function. no, the relation is not a function. the domain value of 2 is assigned to both -4, and 5.

Explanation:

To determine if a relation is a function, each domain (x - value) must map to exactly one range (y - value). In the given relation \(\{(2, - 4),(-2,4),(2,5),(5,-1),(-1,5)\}\), the domain value \(2\) is paired with both \(-4\) and \(5\). This violates the definition of a function (since one x - value has multiple y - values). The first option is incorrect because \(-1\) maps to \(5\) and \(2\) maps to \(5\) (multiple x - values can map to the same y - value, that's allowed), but the issue is with \(2\) having multiple y - values. The second option is wrong as the relation fails the function test. The third option correctly identifies that the domain value \(2\) is assigned to both \(-4\) and \(5\), so the relation is not a function.

Answer:

No, the relation is not a function. The domain value of 2 is assigned to both -4, and 5.