To determine whether each relation is a function, we need to apply the
vertical line test or check if each input (x-value) corresponds to exactly one output (y-value). Here's the analysis for each image:
---
1. Table
| x | y |
|---|---|
| -5 | -3 |
| -1 | -2 |
| 0 | 4 |
| 3 | 6 |
| 5 | 20 |
- Each x-value appears only once.
-
Conclusion: YES
---
2. Ordered Pairs
{(1, 2), (2, 4), (3, 8), (4, 16), (5, 32)}
- Each x-value appears only once.
-
Conclusion: YES
---
3. Graph
- The graph is a parabola opening upwards.
- A vertical line will intersect the graph at most once.
-
Conclusion: YES
---
4. Mapping Diagram
- Each x-value maps to exactly one y-value.
-
Conclusion: YES
---
5. Graph
- The graph is a straight line.
- A vertical line will intersect the graph at most once.
-
Conclusion: YES
---
6. Mapping Diagram
- The x-value "1" maps to two different y-values (4 and -1).
-
Conclusion: NO
---
7. Graph
- The graph is a parabola opening to the right.
- A vertical line can intersect the graph at more than one point.
-
Conclusion: NO
---
8. Graph
- The graph shows a set of points.
- A vertical line can intersect the graph at more than one point.
-
Conclusion: NO
---
9. Table
| x | y |
|---|---|
| -3 | 2 |
| 0 | 2 |
| 1 | 2 |
| 2 | 2 |
- Each x-value appears only once.
-
Conclusion: YES
---
10. Ordered Pairs
{(2, -1), (3, 7), (2, 4)}
- The x-value "2" appears twice with different y-values (-1 and 4).
-
Conclusion: NO
---
11. Ordered Pairs
{(1, 3), (8, -4), (1, -7)}
- The x-value "1" appears twice with different y-values (3 and -7).
-
Conclusion: NO
---
12. Graph
- The graph is a sine wave.
- A vertical line can intersect the graph at more than one point.
-
Conclusion: NO
---
13. Mapping Diagram
- Each x-value maps to exactly one y-value.
-
Conclusion: YES
---
14. Graph
- The graph is a sine wave.
- A vertical line can intersect the graph at more than one point.
-
Conclusion: NO
---
15. Graph
- The graph is a straight line.
- A vertical line will intersect the graph at most once.
-
Conclusion: YES
---
16. Table
| x | y |
|---|---|
| -2 | 4 |
| 0 | 4 |
| 0 | -4 |
| 2 | 4 |
- The x-value "0" appears twice with different y-values (4 and -4).
-
Conclusion: NO
---
17. Graph
- The graph shows a single point at the origin.
- A vertical line will intersect the graph at most once.
-
Conclusion: YES
---
18. Ordered Pairs
{(2, 4), (6, 6), (12, 9)}
- Each x-value appears only once.
-
Conclusion: YES
---
19. Graph
- The graph shows multiple points.
- A vertical line can intersect the graph at more than one point.
-
Conclusion: NO
---
20. Graph
- The graph shows multiple points.
- A vertical line can intersect the graph at more than one point.
-
Conclusion: NO
---
Final Answers
1. YES
2. YES
3. YES
4. YES
5. YES
6. NO
7. NO
8. NO
9. YES
10. NO
11. NO
12. NO
13. YES
14. NO
15. YES
16. NO
17. YES
18. YES
19. NO
20. NO
$$
\boxed{\text{YES, YES, YES, YES, YES, NO, NO, NO, YES, NO, NO, NO, YES, NO, YES, NO, YES, YES, NO, NO}}
$$
Parent Tip: Review the logic above to help your child master the concept of function or not a function worksheet with answers.
