Question
The table shown at the right gives y as a function of x, that is, yequalsf(x). Use the table to answer parts a through d below.
x
negative 9
negative 5
negative 7
7
13
21
26
y equals f left parenthesis x right parenthesis
2
5
7
1
10
9
14
c. State the domain of this function.
A.
The domain is a finite set of elements. The domain is {
negative 9 comma negative 5 comma negative 7 comma 7 comma 13 comma 21 comma 26}. (Use a comma to separate answers as needed.)
B.
The domain is an interval. The domain is
enter your response here. (Type your answer in interval notation.)
Part 4
State the range of this function.
A.
The range is a finite set of elements. The range is StartSet nothing EndSet
. (Use a comma to separate answers as needed.)
B.
The range is an interval. The range is
enter your response here. (Type your answer in interval notation.)
Part 5
d. Explain why this relationship describes y as a function of x. Choose the correct answer below.
A.
Each input gives exactly one output.
B.
Each input gives more than one output.
C.
Each input gives exactly two outputs.
Choose the correct answer below.Choose the correct answer below.input field 1input field 2State the domain of this function.input field 3input field 4State the range of this function.Choose the correct answer below.
x
negative 9
negative 5
negative 7
7
13
21
26
y equals f left parenthesis x right parenthesis
2
5
7
1
10
9
14
c. State the domain of this function.
A.
The domain is a finite set of elements. The domain is {
negative 9 comma negative 5 comma negative 7 comma 7 comma 13 comma 21 comma 26}. (Use a comma to separate answers as needed.)
B.
The domain is an interval. The domain is
enter your response here. (Type your answer in interval notation.)
Part 4
State the range of this function.
A.
The range is a finite set of elements. The range is StartSet nothing EndSet
. (Use a comma to separate answers as needed.)
B.
The range is an interval. The range is
enter your response here. (Type your answer in interval notation.)
Part 5
d. Explain why this relationship describes y as a function of x. Choose the correct answer below.
A.
Each input gives exactly one output.
B.
Each input gives more than one output.
C.
Each input gives exactly two outputs.
Choose the correct answer below.Choose the correct answer below.input field 1input field 2State the domain of this function.input field 3input field 4State the range of this function.Choose the correct answer below.
Answers
GPT-4o mini
Based on the provided data for \(f(x)\):
- \(x: -9, -5, -7, 7, 13, 21, 26\)
- \(y = f(x): 2, 5, 7, 1, 10, 9, 14\)
Let's answer parts a through d:
### Part C: State the Domain of the Function
***Domain:***
The input values of \(x\) in the given data set are:
\[
\{-9, -5, -7, 7, 13, 21, 26\}
\]
This is a finite set of elements; therefore, the answer is:
**A.** The domain is a finite set of elements:
\(\{-9, -5, -7, 7, 13, 21, 26\}\)
### Part 4: State the Range of the Function
***Range:***
The output values of \(y\) in the given data set are:
\[
\{2, 5, 7, 1, 10, 9, 14\}
\]
This is also a finite set of elements; thus, the answer is:
**A.** The range is a finite set of elements:
\(\{1, 2, 5, 7, 9, 10, 14\}\)
### Part 5: Explain Why This Relationship Describes \(y\) as a Function of \(x\)
To describe \(y\) as a function of \(x\), we need to determine whether each input corresponds to exactly one output. Since each input \(x\) in the provided data has a unique output \(y\) associated with it, the correct answer is:
**A.** Each input gives exactly one output.
### Summary of Answers
- **Domain:** \(\{-9, -5, -7, 7, 13, 21, 26\}\)
- **Range:** \(\{1, 2, 5, 7, 9, 10, 14\}\)
- **Explanation:** Each input gives exactly one output.
- \(x: -9, -5, -7, 7, 13, 21, 26\)
- \(y = f(x): 2, 5, 7, 1, 10, 9, 14\)
Let's answer parts a through d:
### Part C: State the Domain of the Function
***Domain:***
The input values of \(x\) in the given data set are:
\[
\{-9, -5, -7, 7, 13, 21, 26\}
\]
This is a finite set of elements; therefore, the answer is:
**A.** The domain is a finite set of elements:
\(\{-9, -5, -7, 7, 13, 21, 26\}\)
### Part 4: State the Range of the Function
***Range:***
The output values of \(y\) in the given data set are:
\[
\{2, 5, 7, 1, 10, 9, 14\}
\]
This is also a finite set of elements; thus, the answer is:
**A.** The range is a finite set of elements:
\(\{1, 2, 5, 7, 9, 10, 14\}\)
### Part 5: Explain Why This Relationship Describes \(y\) as a Function of \(x\)
To describe \(y\) as a function of \(x\), we need to determine whether each input corresponds to exactly one output. Since each input \(x\) in the provided data has a unique output \(y\) associated with it, the correct answer is:
**A.** Each input gives exactly one output.
### Summary of Answers
- **Domain:** \(\{-9, -5, -7, 7, 13, 21, 26\}\)
- **Range:** \(\{1, 2, 5, 7, 9, 10, 14\}\)
- **Explanation:** Each input gives exactly one output.