Question
Is it linear non linear a function or not a function:
3 hours - 5 Celsius
6 hours - 0 Celsius
9 hours - -5 Celsius
12 hours - 10 Celsisu
3 hours - 5 Celsius
6 hours - 0 Celsius
9 hours - -5 Celsius
12 hours - 10 Celsisu
Answers
GPT-4o mini
To determine whether the given relationship represents a function and whether it is linear or nonlinear, let's analyze the data provided:
We have the following points:
1. (3, -5)
2. (6, 0)
3. (9, -5)
4. (12, 10)
**Step 1: Is it a function?**
A relation is a function if each input (the first value, representing hours in this case) corresponds to exactly one output (the second value, corresponding to degrees Celsius).
Looking at the data:
- Each hour (3, 6, 9, and 12) is associated with exactly one temperature.
- Thus, these points do represent a function.
**Step 2: Is it linear or nonlinear?**
To determine if the function is linear, we can check if the change in output (temperature) is consistent with the change in input (hours). Specifically, we can calculate the slope between the points:
1. From (3, -5) to (6, 0):
- Change in y = 0 - (-5) = 5
- Change in x = 6 - 3 = 3
- Slope = Change in y / Change in x = 5 / 3 ≈ 1.67
2. From (6, 0) to (9, -5):
- Change in y = -5 - 0 = -5
- Change in x = 9 - 6 = 3
- Slope = -5 / 3 ≈ -1.67
3. From (9, -5) to (12, 10):
- Change in y = 10 - (-5) = 15
- Change in x = 12 - 9 = 3
- Slope = 15 / 3 = 5
Since the slopes between the points are not consistent (they change), the function is not linear.
**Conclusion:**
1. It **is a function**.
2. It is **not a linear function**; it is a **nonlinear function**.
We have the following points:
1. (3, -5)
2. (6, 0)
3. (9, -5)
4. (12, 10)
**Step 1: Is it a function?**
A relation is a function if each input (the first value, representing hours in this case) corresponds to exactly one output (the second value, corresponding to degrees Celsius).
Looking at the data:
- Each hour (3, 6, 9, and 12) is associated with exactly one temperature.
- Thus, these points do represent a function.
**Step 2: Is it linear or nonlinear?**
To determine if the function is linear, we can check if the change in output (temperature) is consistent with the change in input (hours). Specifically, we can calculate the slope between the points:
1. From (3, -5) to (6, 0):
- Change in y = 0 - (-5) = 5
- Change in x = 6 - 3 = 3
- Slope = Change in y / Change in x = 5 / 3 ≈ 1.67
2. From (6, 0) to (9, -5):
- Change in y = -5 - 0 = -5
- Change in x = 9 - 6 = 3
- Slope = -5 / 3 ≈ -1.67
3. From (9, -5) to (12, 10):
- Change in y = 10 - (-5) = 15
- Change in x = 12 - 9 = 3
- Slope = 15 / 3 = 5
Since the slopes between the points are not consistent (they change), the function is not linear.
**Conclusion:**
1. It **is a function**.
2. It is **not a linear function**; it is a **nonlinear function**.