To determine whether each relation is a function, we need to check if each input (x-value) corresponds to exactly one output (y-value). A relation is a function if no input is paired with more than one output.
Let's analyze each problem step by step:
---
Problem 1:
| x | y |
|---|---|
| 5 | 1 |
| 5 | 2 |
| 5 | 3 |
| 5 | 4 |
-
Analysis: The input `x = 5` is paired with multiple outputs (`1, 2, 3, 4`).
-
Conclusion: This is
not a function.
---
Problem 2:
Input → Output:
- Input: 6 → Output: 9
- Input: 8 → Output: 11
- Input: 11 → Output: 15
- Input: 14 → Output: 20
-
Analysis: Each input has exactly one output.
-
Conclusion: This is a function.
---
Problem 3:
Input → Output:
- Input: -5 → Output: 2
- Input: -2 → Output: 8
- Input: 1 → Output: 7
- Input: 0 → Output: 6
-
Analysis: Each input has exactly one output.
-
Conclusion: This is a function.
---
Problem 4:
Points: (-9, 4), (8, 2), (6, 5), (2, 3)
-
Analysis: Each x-value appears only once:
- x = -9 → y = 4
- x = 8 → y = 2
- x = 6 → y = 5
- x = 2 → y = 3
-
Conclusion: This is a function.
---
Problem 5:
| x | y |
|---|---|
| 6 | -2 |
| 8 | 0 |
| 10 | 2 |
| 12 | -4 |
| 14 | 11 |
-
Analysis: Each input has exactly one output.
-
Conclusion: This is a function.
---
Problem 6:
Input → Output:
- Input: 3 → Output: 2
- Input: 6 → Output: 4
- Input: 9 → Output: 6
- Input: 12 → Output: 6
-
Analysis: Each input has exactly one output.
-
Conclusion: This is a function.
---
Problem 7:
Points: (-11, 14), (13, 14), (1, 14), (8, 11)
-
Analysis: Each x-value appears only once:
- x = -11 → y = 14
- x = 13 → y = 14
- x = 1 → y = 14
- x = 8 → y = 11
-
Conclusion: This is a function.
---
Problem 8:
| x | y |
|---|---|
| -9 | 1 |
| -3 | 1 |
| 0 | 1 |
| -6 | 0 |
-
Analysis: Each input has exactly one output.
-
Conclusion: This is a function.
---
Final Answers:
1. Not a function
2. Function
3. Function
4. Function
5. Function
6. Function
7. Function
8. Function
Boxed Answer:
\[
\boxed{\text{Not a function, Function, Function, Function, Function, Function, Function, Function}}
\]
Parent Tip: Review the logic above to help your child master the concept of determining functions worksheet.
