Question

state the domain and range for the following relation. then determine whether the relation represents a function. {(-7, -1), (-6, -1), (-5, -1), (-4, -1)} the domain of the relation is {}. (use a comma to separate answers as needed.) the range of the relation is {}. (use a comma to separate answers as needed.) does the relation represent a function? choose the correct answer below. a. the relation is not a function because there are ordered pairs with -7 as the first element and different second elements b. the relation is a function because there are no ordered pairs with the same first element and different second elements. c. the relation is a function because there are no ordered pairs with the same second element and different first elements. d. the relation is not a function because there are ordered pairs with -1 as the second element and different first elements.

Explanation:

Step1: Find the domain

The domain of a relation is the set of all first elements (x - values) of the ordered pairs. For the relation \(\{(-7, -1), (-6, -1), (-5, -1), (-4, -1)\}\), the first elements are -7, -6, -5, -4. So the domain is \(\{-7, -6, -5, -4\}\).

Step2: Find the range

The range of a relation is the set of all second elements (y - values) of the ordered pairs. For the given relation, the second element in each ordered pair is -1. So the range is \(\{-1\}\).

Step3: Determine if it's a function

A relation is a function if each first element (input) is paired with exactly one second element (output). In this relation, each of the first elements (-7, -6, -5, -4) is paired with only -1. There are no two ordered pairs with the same first element and different second elements. So the relation is a function, and the correct reasoning is given in option B.

Answer:

The domain of the relation is \(\{-7, -6, -5, -4\}\).
The range of the relation is \(\{-1\}\).
Does the relation represent a function? B. The relation is a function because there are no ordered pairs with the same first element and different second elements.