Printable math worksheet titled 'Functions - Ordered Pairs' that asks students to determine if given sets of coordinates and plotted graphs represent functions.

Let’s solve this step by step.

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## Part A: State whether each set of ordered pairs represents a function.

🔑 Key Concept:

A function is a relation where each input (x-value) has exactly one output (y-value).
If any x-value appears more than once with different y-values, it is NOT a function.

We’ll go through each set:

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1) { (10, 9), (–2, –16), (–6, 7), (5, 8), (8, –16), (–11, 9) }

✔ All x-values are unique: 10, –2, –6, 5, 8, –11 → No repeats

→ This IS a function.

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2) { (–7, 4), (–8, 3), (–7, 7), (–20, 8), (5, 9), (3, 1), (2, 6) }

✘ x = –7 appears twice: (–7, 4) and (–7, 7) → Different y-values for same x

→ This is NOT a function.

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3) { (–13, 4), (7, –15), (–13, 9), (6, –12), (–18, 0) }

✘ x = –13 appears twice: (–13, 4) and (–13, 9)

→ This is NOT a function.

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4) { (15, –3), (–6, 9), (–3, 0), (–1, 16) }

✔ All x-values: 15, –6, –3, –1 → All unique

→ This IS a function.

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5) { (–4, 3), (5, –9), (11, 4), (9, 6), (5, –3), (8, –9), (1, 4) }

✘ x = 5 appears twice: (5, –9) and (5, –3)

→ This is NOT a function.

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6) { (12, –18), (15, 1), (12, 5), (0, 9), (–5, –17) }

✘ x = 12 appears twice: (12, –18) and (12, 5)

→ This is NOT a function.

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7) { (6, 0), (–12, –16), (–6, 10), (20, –7) }

✔ All x-values: 6, –12, –6, 20 → All unique

→ This IS a function.

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8) { (–2, –4), (–8, 3), (–7, –4), (–2, –8), (11, 8), (9, –4) }

✘ x = –2 appears twice: (–2, –4) and (–2, –8)

→ This is NOT a function.

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## ✔ Part A Answers:

1) Yes
2) No
3) No
4) Yes
5) No
6) No
7) Yes
8) No

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## Part B: State whether each set of ordered pairs on the graph represents a function.

🔑 Key Concept:

Use the Vertical Line Test:
If any vertical line intersects the graph at more than one point, then it is NOT a function.

We’ll analyze each graph:

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Graph 1:

Looking at the points plotted:
- At x = –10 → y = –10
- At x = –8 → y = –6
- At x = –6 → y = –2
- At x = –4 → y = 2
- At x = –2 → y = 6
- At x = 0 → y = 10
- At x = 2 → y = 14
- At x = 4 → y = 18
- At x = 6 → y = 22

✔ Every x has only one y-value → Passes Vertical Line Test

→ This IS a function.

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Graph 2:

Points include:
- x = –6 → y = 6
- x = –4 → y = 2
- x = –2 → y = –2
- x = 0 → y = –6
- x = 2 → y = –10
- x = 4 → y = –14
- x = 6 → y = –18
- x = 8 → y = –22

✔ All x-values are unique → Only one y per x

→ This IS a function.

*(Note: Even though it’s decreasing, as long as no x repeats with different y, it’s fine.)*

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Graph 3:

Look carefully — there’s a problem!

At x = 2, there are two points: one at y = 6 and another at y = –6?
Wait — let’s check the grid.

Actually, looking closely at Graph 3:

- At x = –6 → y = 6
- At x = –4 → y = 2
- At x = –2 → y = –2
- At x = 0 → y = –6
- At x = 2 → y = –2 AND also y = 6? ❗

Wait — actually, in the image, at x=2, there are two distinct points: one at (2, 6) and another at (2, –2)?
That would mean same x, two different y’s → Fails Vertical Line Test

✔ Let’s verify: Yes — if you draw a vertical line at x=2, it hits two points.

→ This is NOT a function.

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## ✔ Part B Answers:

1) Yes
2) Yes
3) No

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## 📝 Final Answers:

A)

1) Yes
2) No
3) No
4) Yes
5) No
6) No
7) Yes
8) No

B)

1) Yes
2) Yes
3) No

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Let me know if you’d like a visual explanation or want to practice more!