Question
Is the relation shown in the table a function?
x f(x)
32
01
5-7
-3 2
(1 point)
Yes, every output has one unique input.
Yes, every input has one unique output.
No, there are multiple inputs with the same output.
No, there are multiple outputs with the same input.
x f(x)
32
01
5-7
-3 2
(1 point)
Yes, every output has one unique input.
Yes, every input has one unique output.
No, there are multiple inputs with the same output.
No, there are multiple outputs with the same input.
Answers
Answer
Read the given scenarios. Determine if it is a function or not a function. (4 points)
Function
Not a Function
Input is Student ID number. Output is student age.
The teacher surveys the class. The input is the ages of students in class.
The output is the grade level of students in class.
Input is the year a group of students graduates from high school. Output is a list of their current salaries.
Input is your birthday. Output is number of TVs in your house.
Function
Not a Function
Input is Student ID number. Output is student age.
The teacher surveys the class. The input is the ages of students in class.
The output is the grade level of students in class.
Input is the year a group of students graduates from high school. Output is a list of their current salaries.
Input is your birthday. Output is number of TVs in your house.
Answered by
GPT-4o mini
To determine whether the relation shown in the table is a function, we need to check for the following:
1. A function must have one unique output (f(x)) for every input (x).
2. There cannot be the same input associated with different outputs.
From the provided data, we have:
- \( f(32) \): output unknown
- \( f(0) = 1 \)
- \( f(5) = -7 \)
- \( f(-3) = 2 \)
There is no indication that any input corresponds to more than one output. Thus:
- \( 0 \) maps to \( 1 \)
- \( 5 \) maps to \( -7 \)
- \( -3 \) maps to \( 2 \)
However, we do not have the output for \( x = 32 \). Since we cannot assess whether there are multiple outputs for every input based on the provided data, let's focus on what we do have.
Based on the provided information:
1. Each input (0, 5, -3) has a unique output.
2. There are no repeated inputs with different outputs shown.
Thus, based on the definition of a function where each input corresponds to one and only one output, the correct answer is:
**Yes, every input has one unique output.**
1. A function must have one unique output (f(x)) for every input (x).
2. There cannot be the same input associated with different outputs.
From the provided data, we have:
- \( f(32) \): output unknown
- \( f(0) = 1 \)
- \( f(5) = -7 \)
- \( f(-3) = 2 \)
There is no indication that any input corresponds to more than one output. Thus:
- \( 0 \) maps to \( 1 \)
- \( 5 \) maps to \( -7 \)
- \( -3 \) maps to \( 2 \)
However, we do not have the output for \( x = 32 \). Since we cannot assess whether there are multiple outputs for every input based on the provided data, let's focus on what we do have.
Based on the provided information:
1. Each input (0, 5, -3) has a unique output.
2. There are no repeated inputs with different outputs shown.
Thus, based on the definition of a function where each input corresponds to one and only one output, the correct answer is:
**Yes, every input has one unique output.**
Answered by
GPT-4o mini
Let's analyze each scenario to determine if it represents a function or not:
1. **Input is Student ID number. Output is student age.**
- **Function:** Each student ID corresponds to exactly one student and therefore one unique age.
2. **The teacher surveys the class. The input is the ages of students in class. The output is the grade level of students in class.**
- **Not a Function:** Multiple students can be the same age but belong to different grade levels (e.g., kids of the same age can be in different grades). Hence, the same age (input) can yield different grade levels (outputs).
3. **Input is the year a group of students graduates from high school. Output is a list of their current salaries.**
- **Not a Function:** A single graduation year (input) can correspond to multiple students who may have different current salaries (outputs). Thus, it does not have a unique output.
4. **Input is your birthday. Output is the number of TVs in your house.**
- **Not a Function:** While it's possible for one specific birthday to indicate one number of TVs, many people with the same birthday could have different numbers of TVs in their homes. Therefore, the same birthday can yield different outputs.
### Summary:
- **Function:** Input is Student ID number. Output is student age.
- **Not a Function:**
- The teacher surveys the class (ages to grade levels).
- Input is the year a group of students graduates from high school (graduation year to salaries).
- Input is your birthday (birthday to number of TVs in your house).
1. **Input is Student ID number. Output is student age.**
- **Function:** Each student ID corresponds to exactly one student and therefore one unique age.
2. **The teacher surveys the class. The input is the ages of students in class. The output is the grade level of students in class.**
- **Not a Function:** Multiple students can be the same age but belong to different grade levels (e.g., kids of the same age can be in different grades). Hence, the same age (input) can yield different grade levels (outputs).
3. **Input is the year a group of students graduates from high school. Output is a list of their current salaries.**
- **Not a Function:** A single graduation year (input) can correspond to multiple students who may have different current salaries (outputs). Thus, it does not have a unique output.
4. **Input is your birthday. Output is the number of TVs in your house.**
- **Not a Function:** While it's possible for one specific birthday to indicate one number of TVs, many people with the same birthday could have different numbers of TVs in their homes. Therefore, the same birthday can yield different outputs.
### Summary:
- **Function:** Input is Student ID number. Output is student age.
- **Not a Function:**
- The teacher surveys the class (ages to grade levels).
- Input is the year a group of students graduates from high school (graduation year to salaries).
- Input is your birthday (birthday to number of TVs in your house).