Which table of values appears to show a linear function?

Question

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)

Answer 1

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.

Answer 2

are u sure its A?

Answer 3

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!