Practice worksheet for identifying functions in various representations including tables, mapping diagrams, and ordered pairs.

Let's go through each of the 8 problems and determine whether each relation is a function.

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🔎 Definition: What is a Function?

A function is a relation where each input (x-value) has exactly one output (y-value).
In other words:
- No x-value can be paired with more than one y-value.
- If any x-value appears more than once with different y-values, it’s not a function.

We’ll check each one:

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1. Table:

```
x | y
5 | 1
5 | 2
5 | 3
5 | 4
```

- The same x-value (5) maps to multiple y-values: 1, 2, 3, 4.
- ✘ Not a function

> ✔ Answer: No, not a function.

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2. Mapping Diagram (input → output):

- Input: 6 → 9, 11
- Input: 8 → 11, 15
- Input: 11 → 15, 20
- Input: 14 → 9, 20

Each input maps to two outputs.

- For example: 6 goes to both 9 and 11 → multiple outputs for one input.
- ✘ Not a function

> ✔ Answer: No, not a function.

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3. Mapping Diagram:

Input: -5, -2, 1, 0
Output: 2, 8, 7, 6

Check if any input maps to more than one output:
- -5 → 2
- -2 → 8
- 1 → 7
- 0 → 6

Wait — look closely:
- -5 → 2
- -2 → 8
- 1 → 7
- 0 → 6

But also:
- -5 → 6? Wait — no! Let's trace the lines.

From diagram:
- -5 → 2
- -2 → 8
- 1 → 7
- 0 → 6

But wait — does any input go to more than one output?

Actually, looking at the diagram:
- -5 → 2
- -2 → 8
- 1 → 7
- 0 → 6

And also:
- -5 → 6? No — only one arrow from each input.

Wait — actually, let’s recheck:
- -5 → 2
- -2 → 8
- 1 → 7
- 0 → 6

But 1 has two arrows: one to 7, and one to 6? Wait — no!

Looking carefully:
The diagram shows:
- -5 → 2
- -2 → 8
- 1 → 7
- 0 → 6

But 1 has an arrow to 7 and also to 6? That would be a problem.

Wait — the diagram shows:
- -5 → 2
- -2 → 8
- 1 → 7
- 0 → 6

But also:
- -5 → 6?
- 0 → 7?

Wait — no, there are crossing lines. Let's interpret:

From the diagram:
- -5 → 2
- -2 → 8
- 1 → 7
- 0 → 6

But also:
- -5 → 6? No — only one line from -5 to 2
- -2 → 7? No
- 1 → 6? Yes — there's a line from 1 to 6
- 0 → 7? Yes — line from 0 to 7

So:
- -5 → 2
- -2 → 8
- 1 → 7 and 6 → two outputs!
- 0 → 6 and 7 → two outputs!

Yes! So:
- Input 1 maps to both 7 and 6
- Input 0 maps to both 6 and 7

That means multiple outputs per input → ✘ Not a function

> ✔ Answer: No, not a function.

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4. Ordered Pairs:

(-9, 4), (2, 8), (0, 1), (6, 5), (2, 3)

Look at the x-values:
- -9 → 4
- 2 → 8
- 0 → 1
- 6 → 5
- 2 → 3

So x = 2 appears twice: once with y = 8, once with y = 3 → two different outputs for same input

✘ Not a function

> ✔ Answer: No, not a function.

---

5. Table:

```
x | y
6 | -4
8 | 2
10| 6
12| -4
14| 11
```

Check x-values: all unique: 6, 8, 10, 12, 14

Even though y = -4 appears twice (for x=6 and x=12), that's okay — different inputs can have same output.

✔ Each x has only one y → This is a function

> ✔ Answer: Yes, it is a function.

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6. Mapping Diagram:

Input: 3, 6, 9, 12
Output: 2, 4, 6

Check each input:
- 3 → 2
- 6 → 4
- 9 → 6
- 12 → 2

All inputs map to only one output.

Even though 2 appears twice (from 3 and 12), that’s fine — same output for different inputs is allowed.

✔ This is a function.

> ✔ Answer: Yes, it is a function.

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7. Ordered Pairs:

(-11, 14), (-13, 14), (3, 12), (1, 14), (8, 11)

List x-values:
- -11 → 14
- -13 → 14
- 3 → 12
- 1 → 14
- 8 → 11

All x-values are unique → no repeats.

Even though y = 14 appears multiple times, that’s okay.

✔ Each x has one y → This is a function

> ✔ Answer: Yes, it is a function.

---

8. Table:

```
x | y
-9 | 4
-8 | 3
-8 | 1
-6 | 0
-4 | -3
```

Now, look at x = -8:
- First row: -8 → 3
- Second row: -8 → 1

Same input (-8) has two different outputs (3 and 1)

✘ Not a function

> ✔ Answer: No, not a function.

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✔ Final Answers:

| Problem | Is it a Function? |
|--------|-------------------|
| 1 | ✘ No |
| 2 | ✘ No |
| 3 | ✘ No |
| 4 | ✘ No |
| 5 | ✔ Yes |
| 6 | ✔ Yes |
| 7 | ✔ Yes |
| 8 | ✘ No |

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📝 Summary:

To determine if a relation is a function:
- Check if any x-value appears more than once with different y-values.
- If yes → Not a function
- If all x-values are unique or repeat with same y → Function

Let me know if you'd like this in a printable format or need help graphing them!