Question
Determine whether the data in the diagram is a function, and state the domain and range.
8,2
7,3
6,2
5,2
Responses
No, it is not a function. The domain is the set {8,7,6,5}. The range is the set {−1,3,2}.
No, it is not a function. The domain is the set {−1,3,2}. The range is the set {8,7,6,5}
Yes, it is a function. The domain is the set {8,7,6,5}. The range is the set {−1,3,2}
Yes, it is a function. The domain is the set {-1, 3, 2}. The range is the set {8, 7, 6, 5}
8,2
7,3
6,2
5,2
Responses
No, it is not a function. The domain is the set {8,7,6,5}. The range is the set {−1,3,2}.
No, it is not a function. The domain is the set {−1,3,2}. The range is the set {8,7,6,5}
Yes, it is a function. The domain is the set {8,7,6,5}. The range is the set {−1,3,2}
Yes, it is a function. The domain is the set {-1, 3, 2}. The range is the set {8, 7, 6, 5}
Answers
GPT-4o mini
To determine if the given data represents a function, we need to check if each input (first value) has exactly one output (second value).
The given pairs are:
- (8, 2)
- (7, 3)
- (6, 2)
- (5, 2)
In this case:
- The input 8 maps to the output 2.
- The input 7 maps to the output 3.
- The input 6 maps to the output 2.
- The input 5 maps to the output 2.
The inputs are {8, 7, 6, 5}, which are unique, but the output 2 is associated with both 8 and 6, which means that the same input can produce different outputs (which is allowed), but every input is associated with one output.
Thus, this data can be considered a function, as each input corresponds to exactly one output.
Now, let's identify the domain and range:
- The **domain** is the set of all first elements (inputs): {8, 7, 6, 5}.
- The **range** is the set of all second elements (outputs): {2, 3}.
Now we can evaluate the responses provided:
1. **No, it is not a function. The domain is the set {8,7,6,5}. The range is the set {−1, 3, 2}.**
- Incorrect, as it is indeed a function, and the range is not correctly listed.
2. **No, it is not a function. The domain is the set {−1,3,2}. The range is the set {8, 7, 6, 5}**
- Incorrect. It's still a function, and the domain and range are incorrectly listed.
3. **Yes, it is a function. The domain is the set {8,7,6,5}. The range is the set {−1,3,2}.**
- Incorrect, it correctly identifies it as a function but has an incorrect range.
4. **Yes, it is a function. The domain is the set {-1, 3, 2}. The range is the set {8, 7, 6, 5}.**
- Incorrect. It incorrectly identifies the domain and range.
Hence, the correct conclusion is:
**Yes, it is a function. The domain is {8, 7, 6, 5}, and the range is {2, 3}.** (This option is not explicitly given.)
The given pairs are:
- (8, 2)
- (7, 3)
- (6, 2)
- (5, 2)
In this case:
- The input 8 maps to the output 2.
- The input 7 maps to the output 3.
- The input 6 maps to the output 2.
- The input 5 maps to the output 2.
The inputs are {8, 7, 6, 5}, which are unique, but the output 2 is associated with both 8 and 6, which means that the same input can produce different outputs (which is allowed), but every input is associated with one output.
Thus, this data can be considered a function, as each input corresponds to exactly one output.
Now, let's identify the domain and range:
- The **domain** is the set of all first elements (inputs): {8, 7, 6, 5}.
- The **range** is the set of all second elements (outputs): {2, 3}.
Now we can evaluate the responses provided:
1. **No, it is not a function. The domain is the set {8,7,6,5}. The range is the set {−1, 3, 2}.**
- Incorrect, as it is indeed a function, and the range is not correctly listed.
2. **No, it is not a function. The domain is the set {−1,3,2}. The range is the set {8, 7, 6, 5}**
- Incorrect. It's still a function, and the domain and range are incorrectly listed.
3. **Yes, it is a function. The domain is the set {8,7,6,5}. The range is the set {−1,3,2}.**
- Incorrect, it correctly identifies it as a function but has an incorrect range.
4. **Yes, it is a function. The domain is the set {-1, 3, 2}. The range is the set {8, 7, 6, 5}.**
- Incorrect. It incorrectly identifies the domain and range.
Hence, the correct conclusion is:
**Yes, it is a function. The domain is {8, 7, 6, 5}, and the range is {2, 3}.** (This option is not explicitly given.)