Questions: State the domain and range for the following relation. Then determine whether the relation represents a function. (-9,5),(-9,7),(0,4),(7,8) The domain of the relation is β. (Use a comma to separate answers as needed.) The range of the relation is B. (Use a comma to separate answers as needed.) Does the relation represent a function? Choose the correct answer below. A. The relation is a function because there are no ordered pairs with the same first element and different second elements. B. The relation is not a function because there are ordered pairs with -9 as the first element and different second elements. C. The relation is not a function because there are ordered pairs with 4 as the second element and different first elements. D. The relation is a function because there are no ordered pairs with the same second element and different first elements.

State the domain and range for the following relation. Then determine whether the relation represents a function.
(-9,5),(-9,7),(0,4),(7,8)

The domain of the relation is β.
(Use a comma to separate answers as needed.)
The range of the relation is B.
(Use a comma to separate answers as needed.)
Does the relation represent a function? Choose the correct answer below.
A. The relation is a function because there are no ordered pairs with the same first element and different second elements.
B. The relation is not a function because there are ordered pairs with -9 as the first element and different second elements.
C. The relation is not a function because there are ordered pairs with 4 as the second element and different first elements.
D. The relation is a function because there are no ordered pairs with the same second element and different first elements.

Transcript text: State the domain and range for the following relation. Then determine whether the relation represents a function. \[ \{(-9,5),(-9,7),(0,4),(7,8)\} \] The domain of the relation is $\square$ $\beta$. (Use a comma to separate answers as needed.) The range of the relation is $\square$ B. (Use a comma to separate answers as needed.) Does the relation represent a function? Choose the correct answer below. A. The relation is a function because there are no ordered pairs with the same first element and different second elements. B. The relation is not a function because there are ordered pairs with -9 as the first element and different second elements. C. The relation is not a function because there are ordered pairs with 4 as the second element and different first elements. D. The relation is a function because there are no ordered pairs with the same second element and different first elements.

Solution

Solution Steps

To solve this problem, we need to identify the domain and range of the given set of ordered pairs. The domain consists of all the first elements of the pairs, and the range consists of all the second elements. To determine if the relation is a function, we check if any first element is repeated with different second elements.

Step 1: Identify the Domain

The domain of the relation is the set of all first elements from the ordered pairs. From the given relation $\{(-9, 5), (-9, 7), (0, 4), (7, 8)\}$, the first elements are $-9$, $0$, and $7$. Therefore, the domain is: \[ \text{Domain} = \{-9, 0, 7\} \]

Step 2: Identify the Range

The range of the relation is the set of all second elements from the ordered pairs. The second elements from the relation are $5$, $7$, $4$, and $8$. Thus, the range is: \[ \text{Range} = \{4, 5, 7, 8\} \]

Step 3: Determine if the Relation is a Function

A relation is a function if each first element corresponds to exactly one second element. In this case, the first element $-9$ appears with two different second elements ($5$ and $7$). Therefore, the relation does not satisfy the definition of a function.