Asked by hm
Which table of values appears to show a linear function?
Responses
A A onlyA only
B C onlyC only
C A and BA and B
D A and CA and C
Question 2
Which set of values appears to show a nonlinear function?
Responses
A (1, 1), (2, 4), (3, 9), and (4, 16)(1, 1), (2, 4), (3, 9), and (4, 16)
B (2, 5), (3.5, 8), (4, 9), and (4.5, 10)(2, 5), (3.5, 8), (4, 9), and (4.5, 10)
C (1, 2), (2, −1), (4, −7), and (6, −13)(1, 2), (2, −1), (4, −7), and (6, −13)
D (−2, 3), (8, −2), (10, −3), and (20, −8)
Responses
A A onlyA only
B C onlyC only
C A and BA and B
D A and CA and C
Question 2
Which set of values appears to show a nonlinear function?
Responses
A (1, 1), (2, 4), (3, 9), and (4, 16)(1, 1), (2, 4), (3, 9), and (4, 16)
B (2, 5), (3.5, 8), (4, 9), and (4.5, 10)(2, 5), (3.5, 8), (4, 9), and (4.5, 10)
C (1, 2), (2, −1), (4, −7), and (6, −13)(1, 2), (2, −1), (4, −7), and (6, −13)
D (−2, 3), (8, −2), (10, −3), and (20, −8)
Answers
Answered by
hm
are u sure its A?
Answered by
GPT-4o mini
To determine which table of values shows a linear function, we need to look for a constant rate of change (slope) between the values. A linear function has points that, when plotted, will form a straight line.
**Question 1: Which table of values appears to show a linear function?**
Without the specific table values provided (A, B, C), I can’t analyze them directly. However, if you want to identify a linear function from given data, check if the difference in y-values divided by the difference in x-values remains constant across all points.
- If you find that the differences are consistent, then that table represents a linear function.
- If the differences vary, it is likely nonlinear.
**Question 2: Which set of values appears to show a nonlinear function?**
Let's look at each option:
A: (1, 1), (2, 4), (3, 9), (4, 16)
- These points appear to follow the pattern \(y = x^2\), which is nonlinear.
B: (2, 5), (3.5, 8), (4, 9), and (4.5, 10)
- This set may also indicate a linear trend, but we need to check for the slope. The changes are not uniform, so it could be linear.
C: (1, 2), (2, -1), (4, -7), and (6, -13)
- These values have a changing difference in y-values for the corresponding x-values which indicates nonlinear behavior.
D: (−2, 3), (8, −2), (10, −3), and (20, −8)
- Similar to C, these values also exhibit a changing difference in y-values, indicating nonlinearity.
Considering these analyses:
The answer to Question 2 would be **A** since it clearly represents a quadratic function, hence is nonlinear.
For Question 1, if you can provide the specific table values for A, B, and C, I can help determine which ones show a linear function.
**Question 1: Which table of values appears to show a linear function?**
Without the specific table values provided (A, B, C), I can’t analyze them directly. However, if you want to identify a linear function from given data, check if the difference in y-values divided by the difference in x-values remains constant across all points.
- If you find that the differences are consistent, then that table represents a linear function.
- If the differences vary, it is likely nonlinear.
**Question 2: Which set of values appears to show a nonlinear function?**
Let's look at each option:
A: (1, 1), (2, 4), (3, 9), (4, 16)
- These points appear to follow the pattern \(y = x^2\), which is nonlinear.
B: (2, 5), (3.5, 8), (4, 9), and (4.5, 10)
- This set may also indicate a linear trend, but we need to check for the slope. The changes are not uniform, so it could be linear.
C: (1, 2), (2, -1), (4, -7), and (6, -13)
- These values have a changing difference in y-values for the corresponding x-values which indicates nonlinear behavior.
D: (−2, 3), (8, −2), (10, −3), and (20, −8)
- Similar to C, these values also exhibit a changing difference in y-values, indicating nonlinearity.
Considering these analyses:
The answer to Question 2 would be **A** since it clearly represents a quadratic function, hence is nonlinear.
For Question 1, if you can provide the specific table values for A, B, and C, I can help determine which ones show a linear function.
Answered by
GPT-4o mini
Let’s analyze the response again for Question 2 in detail:
### Given sets of values:
1. **A**: (1, 1), (2, 4), (3, 9), (4, 16)
- This set represents the function \( y = x^2 \). It is indeed nonlinear.
2. **B**: (2, 5), (3.5, 8), (4, 9), and (4.5, 10)
- The differences between the y-values are:
- 8 - 5 = 3
- 9 - 8 = 1
- 10 - 9 = 1
- The differences are not consistent, suggesting this is nonlinear.
3. **C**: (1, 2), (2, -1), (4, -7), and (6, -13)
- The differences between the y-values indicate a pattern that doesn't follow a straight line:
- -1 - 2 = -3
- -7 - (-1) = -6
- -13 - (-7) = -6
- Not linear.
4. **D**: (−2, 3), (8, −2), (10, −3), and (20, −8)
- The changes in this set also do not display a consistent slope:
- -2 - 3 = -5
- -3 - (-2) = -1
- -8 - (-3) = -5
- Not linear.
### Conclusion for Question 2:
The set that clearly shows a nonlinear pattern is **A** since they follow a quadratic pattern.
If you mean to inquire if all options were reviewed properly, you are correct to ask. However, **A** does represent a nonlinear function.
So, the correct answer for which set appears to show a nonlinear function in Question 2 is **A**, as it follows \( y = x^2 \).
If there's a misunderstanding or specific details you're questioning, please let me know!
### Given sets of values:
1. **A**: (1, 1), (2, 4), (3, 9), (4, 16)
- This set represents the function \( y = x^2 \). It is indeed nonlinear.
2. **B**: (2, 5), (3.5, 8), (4, 9), and (4.5, 10)
- The differences between the y-values are:
- 8 - 5 = 3
- 9 - 8 = 1
- 10 - 9 = 1
- The differences are not consistent, suggesting this is nonlinear.
3. **C**: (1, 2), (2, -1), (4, -7), and (6, -13)
- The differences between the y-values indicate a pattern that doesn't follow a straight line:
- -1 - 2 = -3
- -7 - (-1) = -6
- -13 - (-7) = -6
- Not linear.
4. **D**: (−2, 3), (8, −2), (10, −3), and (20, −8)
- The changes in this set also do not display a consistent slope:
- -2 - 3 = -5
- -3 - (-2) = -1
- -8 - (-3) = -5
- Not linear.
### Conclusion for Question 2:
The set that clearly shows a nonlinear pattern is **A** since they follow a quadratic pattern.
If you mean to inquire if all options were reviewed properly, you are correct to ask. However, **A** does represent a nonlinear function.
So, the correct answer for which set appears to show a nonlinear function in Question 2 is **A**, as it follows \( y = x^2 \).
If there's a misunderstanding or specific details you're questioning, please let me know!