Function vs Not a Function Card Sort Activity | Math = Love - Free Printable

Let's go through each of the given relations and determine whether they are functions or not functions, based on the definition of 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.

We'll evaluate each item in the image and sort them into:
- ✔ FUNCTION
- ✘ NOT A FUNCTION

---

🔹 1. Table:

```
x | 3 3 4 4 5
y |-1 0 -1 2 0
```

- x = 3 appears twice → y = -1 and y = 0 → Same x, different y
- So, not a function

✔ NOT A FUNCTION

---

🔹 2. Set of ordered pairs:

`{(5,1), (-1,5), (-5,1), (1,-5), (5,3)}`

- x = 5 appears twice: (5,1) and (5,3) → same x, different y
- So, not a function

✔ NOT A FUNCTION

---

🔹 3. Set of ordered pairs:

`{(1,4), (3,2), (-3,-2), (1,2), (-2,-3)}`

- x = 1 appears twice: (1,4) and (1,2) → same x, different y
- So, not a function

✔ NOT A FUNCTION

---

🔹 4. Graph: S-shaped curve (like a sideways "S")

- Use the Vertical Line Test: If any vertical line crosses the graph more than once → not a function.
- This graph fails the vertical line test (some vertical lines cross it twice).
- So, not a function

✔ NOT A FUNCTION

---

🔹 5. Graph: Circle centered at origin

- A circle fails the vertical line test (e.g., at x=0, two y-values)
- So, not a function

✔ NOT A FUNCTION

---

🔹 6. Table:

```
x | -1 -2 -3 -4 -5
y |-2 -3 -4 -4 -6
```

- Each x appears only once → each input maps to one output
- Even though y = -4 appears for two x-values, that’s allowed (as long as no x repeats)
- So, this is a function

✔ FUNCTION

---

🔹 7. Set of ordered pairs:

`{(-3,0), (-2,0), (-1,0), (0,0), (1,0)}`

- All x-values are unique → each x maps to exactly one y
- So, this is a function

✔ FUNCTION

---

🔹 8. Graph: Straight line (diagonal from bottom-left to top-right)

- Passes vertical line test → every x has one y
- So, function

✔ FUNCTION

---

🔹 9. Mapping diagram: Inputs → Outputs

Inputs: -2, -1, 4
Outputs: -1, 3, 5, 8
Arrows:
- -2 → -1
- -1 → 3
- 4 → 5
- 4 → 8 → wait! 4 maps to two outputs (5 and 8)

→ Same input (4) has two outputs → not a function

✔ NOT A FUNCTION

---

🔹 10. Table:

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

- Each x has one y → even if all y-values are same, it's fine
- So, this is a function

✔ FUNCTION

---

🔹 11. Mapping diagram: Inputs → Outputs

Inputs: -3, -1, 5, 8
Outputs: 2, 7
Arrows:
- -3 → 2
- -1 → 7
- 5 → 7
- 8 → 7

→ Every input maps to exactly one output → function

✔ FUNCTION

---

🔹 12. Table:

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

- x = 4 appears twice → y = 3 and y = 2 → same x, different y
- So, not a function

✔ NOT A FUNCTION

---

🔹 13. Graph: Parabola opening upward (vertex at origin)

- This is a standard parabola $ y = x^2 $
- Passes vertical line test → every x has one y
- So, function

✔ FUNCTION

---

🔹 14. Table:

```
x | 1 4 6 8 1
y |-2 0 -2 0 -2
```

- x = 1 appears twice: first row (1,-2), last row (1,-2) → same x, same y → okay
- But x = 4 → y = 0, x = 6 → y = -2, etc.
- Wait: x = 1 appears twice, but both times y = -2 → so it's still consistent
- So, this is a function (even if repeated entries, as long as same output)

✔ FUNCTION

---

🔹 15. Set of ordered pairs:

`{(-2,1), (1,-2), (-1,2), (-2,1), (-3,-2)}`

- Note: (-2,1) appears twice → same x, same y → duplicate, but acceptable
- All other x-values are unique
- So, this is a function

✔ FUNCTION

---

## ✔ Final Sorting:

🟩 FUNCTION:

1. Table: `x: -1,-2,-3,-4,-5; y: -2,-3,-4,-4,-6`
2. Set: `{(-3,0), (-2,0), (-1,0), (0,0), (1,0)}`
3. Diagonal line graph
4. Table: `x: -2,-3,-4,-5; y: -1,-1,-1,-1`
5. Mapping diagram: -3→2, -1→7, 5→7, 8→7
6. Parabola graph
7. Table: `x: 1,4,6,8,1; y: -2,0,-2,0,-2`
8. Set: `{(-2,1), (1,-2), (-1,2), (-2,1), (-3,-2)}`

🔴 NOT A FUNCTION:

1. Table: `x: 3,3,4,4,5; y: -1,0,-1,2,0`
2. Set: `{(5,1), (-1,5), (-5,1), (1,-5), (5,3)}`
3. Set: `{(1,4), (3,2), (-3,-2), (1,2), (-2,-3)}`
4. S-shaped graph
5. Circle graph
6. Mapping diagram: 4 → 5 and 8 (same input → multiple outputs)
7. Table: `x: 4,4,5,5; y: 3,2,3,2`

---

## ✔ Summary:

| Item | Type |
|------|------|
| 1. Table (repeated x) | ✘ Not a function |
| 2. Set with (5,1) and (5,3) | ✘ Not a function |
| 3. Set with (1,4) and (1,2) | ✘ Not a function |
| 4. S-shaped graph | ✘ Not a function |
| 5. Circle | ✘ Not a function |
| 6. Table with unique x | ✔ Function |
| 7. Set with unique x | ✔ Function |
| 8. Line graph | ✔ Function |
| 9. Mapping with 4→5 and 8 | ✘ Not a function |
| 10. Constant y table | ✔ Function |
| 11. Mapping with unique inputs | ✔ Function |
| 12. Table with x=4 twice → different y | ✘ Not a function |
| 13. Parabola | ✔ Function |
| 14. Table with x=1 repeated → same y | ✔ Function |
| 15. Set with repeated pair | ✔ Function |

---

✔ Correct Placement:

- FUNCTION box should include:
- The table with x: -1 to -5
- The set {(-3,0), ..., (1,0)}
- The straight line graph
- The constant y table
- The mapping diagram (all inputs map to one output)
- The parabola
- The table with x: 1,4,6,8,1 (repeated x but same y)
- The set with (-2,1) repeated

- NOT A FUNCTION box should include:
- The table with repeated x and different y
- The sets with repeated x and different y
- The S-shaped graph
- The circle
- The mapping diagram with 4 → two outputs
- The table with x=4 → two different y-values

Let me know if you want a visual layout suggestion!