Function Auction Activity | Math = Love - Free Printable

Let's go through each of the 12 items in your "Function or Not a Function?" worksheet and determine whether each represents a function or not a function, based on the definition of a function:

> A function is a relation where each input (x-value) has exactly one output (y-value).
> If any input maps to more than one output, it's not a function.

We'll analyze each item one by one.

---

#1: Table

```
Domain | Range
4 | 3
5 | 4
2 | 5
4 | 6
```

- Input `4` appears twice: once with output `3`, once with output `6`.
- So, one input (4) → two outputs → Not a function

✔ Answer: NOT a function

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#2: Graph (Vertical Line Test)

This is a graph with points plotted:
- Points: (−2, −1), (−1, 0), (0, 1), (1, 2), (2, 3)
- It's a straight line going up.
- Apply vertical line test: Any vertical line crosses only one point.

✔ Answer: FUNCTION

---

#3: Graph (Curve)

It’s a parabola-like curve that opens downward, but it's not a function if it fails the vertical line test.

Wait — actually, this looks like a normal parabola opening down, which is a function because every x has one y.

But let’s check: Is it a single-valued curve?

Yes — even though it goes up and down, each x-value has only one y-value.

So, passes vertical line test.

✔ Answer: FUNCTION

> Note: Only if it were sideways (like a circle or sideways parabola) would it fail.

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#4: Set of Ordered Pairs

{(−1, −2), (0, 1), (1, 4), (3, 7)}

- All x-values are unique: −1, 0, 1, 3 → no repeats
- Each input maps to exactly one output

✔ Answer: FUNCTION

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#5: Mapping Diagram

Input: −1, 0, 2
Output: −2, 1, 3, 4

- −1 → −2
- 0 → 1 and 3? Wait — look carefully.

Actually:
- 0 maps to both 1 and 3 → same input, two outputs

✘ Answer: NOT a function

---

#6: Graph (Grid Plot)

A grid with points: (−2, 2), (−1, 1), (0, 0), (1, 1), (2, 2)

Looks like a V-shape, symmetric about y-axis.

Check vertical line test: Every x has only one y.

Even though (−1,1) and (1,1) have same y, they are different x-values.

Each x has only one y.

✔ Answer: FUNCTION

---

#7: Table

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

All x-values are unique → each input has one output.

✔ Answer: FUNCTION

---

#8: Set of Ordered Pairs

{(1,1), (1,2), (2,1), (2,2)}

- x = 1 → y = 1 and y = 2 → multiple outputs for x=1
- x = 2 → y = 1 and y = 2 → also multiple

So both inputs map to multiple outputs.

✘ Answer: NOT a function

---

#9: Mapping Diagram

Input: 2, 3, 5
Output: 1, 4, 5

- 2 → 1
- 3 → 4
- 5 → 5

Each input maps to exactly one output.

✔ Answer: FUNCTION

---

#10: Set of Ordered Pairs

{(4, −2), (4, −4), (4, 1), (4, 2)}

- All pairs have x = 4, but different y-values
- So one input (4) → four outputs → violates function rule

✘ Answer: NOT a function

---

#11: Table

```
x | y
1 | 1
−1 | 2
0 | 3
−2 | 2
2 | −4
```

All x-values are distinct → no repeated inputs

✔ Answer: FUNCTION

---

#12: Graph (Wavy Curve)

Looks like a sine wave or oscillating curve.

But does it pass the vertical line test?

Yes — even though it goes up and down, every vertical line intersects only once.

So, each x has one y.

✔ Answer: FUNCTION

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✔ Final Answers Summary:

| # | Function? |
|---|----------|
| 1 | ✘ No |
| 2 | ✔ Yes |
| 3 | ✔ Yes |
| 4 | ✔ Yes |
| 5 | ✘ No |
| 6 | ✔ Yes |
| 7 | ✔ Yes |
| 8 | ✘ No |
| 9 | ✔ Yes |
|10 | ✘ No |
|11 | ✔ Yes |
|12 | ✔ Yes |

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🔍 Key Rules Recap:

- Function: Each input has exactly one output.
- Use vertical line test for graphs: if any vertical line hits more than one point → not a function.
- For tables/mappings: check if any x-value repeats with different y-values → not a function.

Let me know if you'd like a visual explanation or printable version!