Function or Not (Yes-No). Interactive worksheet | TopWorksheets - Free Printable

I will solve this problem by examining each of the 20 relations presented in the image and determining whether they are functions or not, based on the definition of a function.

A relation is a function if and only if every input (x-value) has exactly one output (y-value). In other words, no x-value can be paired with more than one y-value. I will check each item against this rule.

I will go through them one by one.

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Items 1-5

Item 1: Table
- x: -5, -1, 0, 5
- y: 3, 2, 1, 7
- Each x has one unique y. ✔️ YES

Item 2: Set of ordered pairs {(2,2), (2,4), (6,8), (8,10)}
- The x-value 2 appears twice: (2,2) and (2,4). ✘ NO

Item 3: Graph
- This is a curve that passes the vertical line test — any vertical line crosses it only once. ✔️ YES

Item 4: Mapping diagram
- Input "s" maps to both "1" and "2". ✘ NO

Item 5: Graph
- A piecewise linear graph. It passes the vertical line test — no vertical line intersects it more than once. ✔️ YES

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Items 6-10

Item 6: Mapping diagram
- Input "6" maps to "4" and "10"; input "5" maps to "4" and "10"; input "2" maps to "10". Multiple outputs for single inputs. ✘ NO

Item 7: Graph (parabola opening right)
- This fails the vertical line test — a vertical line can intersect it at two points. ✘ NO

Item 8: Scatter plot on grid
- Points: (-2, 3), (-1, 1), (0, 0), (1, -1), (2, -3)
- All x-values are unique. ✔️ YES

Item 9: Table
- x: -3, -2, 0, 1, 2
- y: 2, 2, 2, 2, 2
- Each x has one y (even though y is constant). ✔️ YES

Item 10: Set of ordered pairs {(-2,-1), (3,7), (-2,4)}
- x = -2 appears twice: (-2,-1) and (-2,4). ✘ NO

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Items 11-15

Item 11: Set of ordered pairs {(-1,3), (0,-4), (1,-7)}
- All x-values are unique. ✔️ YES

Item 12: Graph (wavy curve)
- Appears to pass the vertical line test — each x has one y. ✔️ YES

Item 13: Mapping diagram
- Input "0" maps to "-1" and "3"; input "2" maps to "5" and "6". ✘ NO

Item 14: Graph (sine wave)
- Passes the vertical line test. ✔️ YES

Item 15: Graph (straight line)
- Clearly passes the vertical line test. ✔️ YES

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Items 16-20

Item 16: Table
- x: 2, 4, 0, -3
- y: 4, 7, 8, 12
- All x-values unique. ✔️ YES

Item 17: Graph (scatter plot)
- Points: (-1, 2), (0, 0), (1, -2), (2, -1)
- All x-values unique. ✔️ YES

Item 18: Set of ordered pairs {(2,4), (6,6), (12,9)}
- All x-values unique. ✔️ YES

Item 19: Mapping diagram
- Input "a" maps to "1" and "3"; input "b" maps to "2" and "4". ✘ NO

Item 20: Graph (cross-shaped scatter plot)
- At x=0, there are multiple y-values (e.g., y=2, y=-2, y=0). Fails vertical line test. ✘ NO

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✔ Final Answer:

Here is the list of answers for each item:

1. YES
2. NO
3. YES
4. NO
5. YES
6. NO
7. NO
8. YES
9. YES
10. NO
11. YES
12. YES
13. NO
14. YES
15. YES
16. YES
17. YES
18. YES
19. NO
20. NO

This completes the solution.