Identifying Functions Worksheets - Free Printable

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

A function is a relation where each input (x-value) corresponds to exactly one output (y-value).
So, if any x-value appears more than once with different y-values, it’s not a function.

We'll go through each set:

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#### 1) {(3,4), (5,–4), (4, 2), (6,6), (–4,–1), (0, –8)}

- All x-values are unique: 3, 5, 4, 6, –4, 0
- No repeated x-values → ✔ This is a function

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#### 2) {(–3, 4), (–4, 8), (–2, 7), (0,6), (6,–5), (1,–3), (3,–5)}

- x-values: –3, –4, –2, 0, 6, 1, 3 → all unique
- No duplicates → ✔ This is a function

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#### 3) {(–12, 12), (7,–13), (–1, 1), (9,–6), (–12,1–10)}

Wait: The last pair says "(-12,1–10)" — this seems like a typo. Probably meant (-12, -10) or (-12, 1-10 = -9)? But likely intended as (-12, -10).

But regardless, look at the first and last pairs:
- (-12, 12) and (-12, -10) → same x = –12, different y-values

→ ✘ Not a function (same input maps to two outputs)

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

- x-values: –1, –3, 5, 1, –8 → all unique
- No repeats → ✔ This is a function

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

Check for repeated x-values:
- x = 4 → appears twice: (4,–1) and (4,–4) → different y-values → ✘ Not a function
- x = 6 → appears twice: (6,–3) and (6,–4) → different y-values → also invalid

Even one duplicate x with different y is enough.

→ ✘ Not a function

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#### 6) {(12,–14), (15, 1), (12, 5), (15,–1), (–5,–17)}

- x = 12 → appears in (12,–14) and (12,5) → different y-values → ✘
- x = 15 → appears in (15,1) and (15,–1) → different y-values → ✘

→ ✘ Not a function

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

- x-values: 6, –1, –4, 9, 20 → all unique → ✔ This is a function

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#### 8) {(–2,–4), (3, 2), (–2,–1), (–4, 2), (1, 1), (8,–4)}

- x = –2 → appears twice: (–2,–4) and (–2,–1) → different y-values → ✘

→ ✘ Not a function

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✔ Summary for Part A:

| Problem | Is it a function? |
|--------|-------------------|
| 1 | Yes |
| 2 | Yes |
| 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.

We need to use the vertical line test:
If any vertical line intersects the graph in more than one point, then it's not a function.

Let’s analyze each graph:

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#### Graph 1:
- Looks like a V-shaped graph (absolute value function)
- It passes the vertical line test: every vertical line hits only one point
- ✔ Function

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#### Graph 2:
- This looks like a sideways parabola (opens left/right)
- For example, at x = 2, there are two points: one above and one below
- Vertical line at x=2 would intersect two points → ✘ Not a function

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#### Graph 3:
- Looks like a straight diagonal line (possibly linear)
- Each x has only one y → passes vertical line test
- ✔ Function

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✔ Summary for Part B:

| Graph | Is it a function? |
|-------|-------------------|
| 1 | Yes |
| 2 | No |
| 3 | Yes |

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✔ Final Answers:

#### Part A:
1. Yes
2. Yes
3. No
4. Yes
5. No
6. No
7. Yes
8. No

#### Part B:
1. Yes
2. No
3. Yes

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