Algebra 2 Worksheets | General Functions Worksheets - Free Printable

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 apply this rule to each problem.

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✔ Problem 1:

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

- The same input (x = 5) maps to multiple outputs (1, 2, 3, 4).
- ✘ Not a function

> Answer: Not a function

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✔ Problem 2:

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

Each input maps to only one output.
- All inputs are unique and have only one arrow.
- ✔️ Yes, it's a function

> Answer: Yes, it's a function

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✔ Problem 3:

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

Wait — look closely:
- Input 1 maps to both 7 and 6?
- From the diagram: 1 has arrows to both 7 and 6?

✔ Wait — let's double-check:
- Arrow from 1 → 7
- Arrow from 1 → 6? Is that correct?

Looking at the diagram:
- Yes, input 1 points to both 7 and 6 → two outputs for one input.

✘ So, one input (1) has two outputs → not a function

> Answer: Not a function

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✔ Problem 4:

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

Check x-values:
- x = -9 → one y
- x = 2 → appears twice: (2,8) and (2,3) → same x, different y

✘ So, x = 2 has two different outputs → not a function

> Answer: Not a function

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✔ Problem 5:

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

Check x-values:
- All x-values are different: 6, 8, 10, 12, 14
- Each x has only one y

✔️ Even though y = -4 appears twice (for x=6 and x=12), that’s allowed — outputs can repeat, but inputs must be unique.

> Answer: Yes, it's a function

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✔ Problem 6:

Input → Output:
- 3 → 2
- 6 → 4
- 9 → 6
- 12 → 4

All inputs are distinct.
- Each input goes to exactly one output.
- Output 4 appears twice (from 6 and 12), but that's fine.

✔️ No input has multiple outputs.

> Answer: Yes, it's a function

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✔ Problem 7:

Ordered pairs:
- (-11, 14)
- (-13, 14)
- (3, 12)
- (1, 14)
- (8, 11)

List x-values:
- -11, -13, 3, 1, 8 → all unique

No repeated x-values → each input has one output.

✔️ Even though y = 14 appears three times, that's okay.

> Answer: Yes, it's a function

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✔ Problem 8:

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

Look at x = -8:
- Appears twice: once with y = 3, once with y = 1

✘ Same input (-8) → two different outputs → not a function

> Answer: Not a function

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✔ Final Answers Summary:

| Problem | Is it a function? | Reason |
|--------|-------------------|--------|
| 1 | ✘ No | x = 5 maps to multiple y-values |
| 2 | ✔ Yes | Each input maps to one output |
| 3 | ✘ No | Input 1 maps to both 6 and 7 |
| 4 | ✘ No | x = 2 appears twice with different y-values |
| 5 | ✔ Yes | All x-values are unique |
| 6 | ✔ Yes | Each input has one output |
| 7 | ✔ Yes | All x-values are unique |
| 8 | ✘ No | x = -8 maps to both 3 and 1 |

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✔ Final Answer Key:

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

Let me know if you'd like this formatted as a worksheet answer key!