Question

find the domain and the range of the relation and d{(6,2),(-5,-4),(1,-1),(3,-7)}the domain is {-5,1,3,6}.(simplify your answers. type an integer or a fractionthe range is {-7,-4,-1,2}.(simplify your answers. type an integer or a fractionis this a function?○ no○ yes

Explanation:

Step1: Recall domain definition

Domain is set of all first elements (x - values) in ordered pairs. Given relation: \(\{(6,2), (-5,-4), (1,-1), (3,-7)\}\), first elements are \(6, -5, 1, 3\). So domain is \(\{-5, 1, 3, 6\}\) (order doesn't matter, but listed as in problem's context).

Step2: Recall range definition

Range is set of all second elements (y - values). Second elements: \(2, -4, -1, -7\). So range is \(\{-7, -4, -1, 2\}\) (order doesn't matter).

Step3: Check if it's a function

A relation is a function if each domain element (x - value) has exactly one range element (y - value). Here, \(6, -5, 1, 3\) are all unique (no repeated x - values), so each x maps to one y. Thus, it is a function.

Answer:

Domain: \(\{-5, 1, 3, 6\}\)
Range: \(\{-7, -4, -1, 2\}\)
Is this a function? Yes