To determine whether each relation is a function, we need to check if each input (x-value) corresponds to exactly one output (y-value). If any input is associated with more than one output, the relation is
not a function.
Let's analyze each problem step by step:
---
Problem 1:
| x | y |
|---|---|
| 5 | 1 |
| 5 | 2 |
| 5 | 3 |
| 5 | 4 |
- The input \( x = 5 \) is associated with multiple outputs: 1, 2, 3, and 4.
-
Conclusion: This is
not a function.
---
Problem 2:
```
input output
6 9
8 11
11 15
14 20
```
- Each input (6, 8, 11, 14) is associated with exactly one output.
-
Conclusion: This is a function.
---
Problem 3:
```
input output
-5 2
-2 8
1 7
0 6
```
- Each input (-5, -2, 1, 0) is associated with exactly one output.
-
Conclusion: This is a function.
---
Problem 4:
```
(-9, 4)
(2, 8)
(0, 1)
(6, 5)
(2, 3)
```
- The input \( x = 2 \) is associated with two outputs: 8 and 3.
-
Conclusion: This is
not a function.
---
Problem 5:
| x | y |
|---|---|
| 6 | -4 |
| 8 | 2 |
| 10 | 6 |
| 12 | -4 |
| 14 | 11 |
- Each input (6, 8, 10, 12, 14) is associated with exactly one output.
-
Conclusion: This is a function.
---
Problem 6:
```
input output
3 2
6 4
9 6
12 6
```
- Each input (3, 6, 9, 12) is associated with exactly one output.
-
Conclusion: This is a function.
---
Problem 7:
```
(-11, 14)
(-13, 14)
(3, 12)
(1, 14)
(8, 11)
```
- Each input (-11, -13, 3, 1, 8) is associated with exactly one output.
-
Conclusion: This is a function.
---
Problem 8:
| x | y |
|---|---|
| -9 | 4 |
| -8 | 3 |
| -8 | 1 |
| -6 | 0 |
| -4 | -3 |
- The input \( x = -8 \) is associated with two outputs: 3 and 1.
-
Conclusion: This is
not a function.
---
Final Answers:
1. Not a function
2. Function
3. Function
4. Not a function
5. Function
6. Function
7. Function
8. Not a function
\[
\boxed{\text{Not a function, Function, Function, Not a function, Function, Function, Function, Not a function}}
\]
Parent Tip: Review the logic above to help your child master the concept of identifying relations and functions worksheet.
