Function or Not (Yes-No) online exercise for - Free Printable

Let's go through each of the 20 problems and determine whether the given relation is a function or not.

---

🔹 Definition:

A relation is a function if each input (x-value) corresponds to exactly one output (y-value).
In other words, no x-value can be paired with more than one y-value.

We'll use this rule for all cases.

---

✔ Answers:

#### 1. Table:
```
x | y
-5 | -3
-1 | -2
0 | 1
-5 | 7
```
- x = -5 appears twice with different y-values (-3 and 7) → ✘ NOT a function

> Answer: NO

---

#### 2. Set: {(1,2), (2,4), (3,6), (4,8), (5,10)}
- All x-values are unique → ✔️ Each x maps to one y

> Answer: YES

---

#### 3. Graph (curve increasing from left to right, like cube root or exponential)
- Passes the vertical line test: any vertical line crosses only once → ✔️ Function

> Answer: YES

---

#### 4. Two circles connected by arrows:
- Left circle: {5, 4} → Right circle: {1}
- Arrows: 5→1, 4→1
- Each x has only one output → ✔️ Function

> Answer: YES

---

#### 5. Graph: Zigzag line (piecewise linear)
- Looks like a continuous graph with sharp turns.
- Vertical line test: every vertical line hits only once → ✔️ Function

> Answer: YES

---

#### 6. Mapping diagram:
- Left: {6, 5, 2, 1} → Right: {-4, -1, 0}
- Arrows:
- 6 → -4
- 5 → -1
- 2 → 0
- 1 → 0
- All inputs map to only one output → ✔️ Function

> Answer: YES

---

#### 7. Graph: Parabola opening sideways (like x = y²)
- This is a sideways parabola.
- A vertical line will cross it twice → ✘ Fails vertical line test

> Answer: NO

---

#### 8. Scatter plot on grid:
- Points: Let's check x-values:
- Look at x-coordinates: some x-values appear multiple times?
- For example, x = 2 might have two points? (Check visually)
- From image: There are two points at x = 2, one at y ≈ 3 and one at y ≈ -1 → ✘ Same x, different y → Not a function

> Answer: NO

---

#### 9. Table:
```
x | y
-3 | 2
0 | 2
1 | 2
2 | 2
```
- All x-values are unique → ✔️ Each x has one y

> Answer: YES

---

#### 10. Set: {(-2,-1), (3,7), (-2,4)}
- x = -2 appears twice with different y-values (-1 and 4) → ✘ NOT a function

> Answer: NO

---

#### 11. Set: {(-1,3), (0,-4), (1,-7)}
- All x-values are unique → ✔️ Function

> Answer: YES

---

#### 12. Graph: Wavy horizontal curve (oscillating up/down)
- Looks like a sine-like wave but horizontal.
- But it’s a function if each x has only one y.
- The graph passes the vertical line test → ✔️ Function

> Answer: YES

---

#### 13. Mapping diagram:
- Left: {-1, 0, 2} → Right: {3, 5, 6}
- Arrows:
- -1 → 3
- 0 → 5
- 2 → 6
- All inputs map to one output → ✔️ Function

> Answer: YES

---

#### 14. Graph: Sine wave (periodic wave)
- Oscillates up and down, but each x has only one y → ✔️ Passes vertical line test

> Answer: YES

---

#### 15. Graph: Line with a break (possibly discontinuous)
- It’s a straight line segment, possibly with a gap.
- Still, each x has only one y → ✔️ Function

> Answer: YES

---

#### 16. Table:
```
x | y
-2 | 4
-1 | 7
0 | 8
-1 | 12
```
- x = -1 appears twice: y = 7 and y = 12 → ✘ Not a function

> Answer: NO

---

#### 17. Scatter plot:
- Points: Let's look at x-values.
- There are multiple points with same x?
- Yes: At least one x-value has two points (e.g., x = 1 has two dots?) → Check carefully
- From image: One point at x=0, one at x=1, one at x=-1, one at x=2 → Wait, looks like:
- x = -2: one point
- x = -1: one point
- x = 0: one point
- x = 1: one point
- x = 2: one point
- All x-values seem unique → ✔️ Function

> Answer: YES

Wait — actually, looking closely: there are four points:
- (-2, ?), (-1, ?), (0, ?), (1, ?), (2, ?) — but seems like no duplicates in x.

So yes → ✔️ Function

> Answer: YES

---

#### 18. Set: {(2,4), (6,6), (12,9)}
- All x-values are unique → ✔️ Function

> Answer: YES

---

#### 19. Mapping diagram:
- Left: {-7, -2, 0, 5} → Right: {-9, -4, -1}
- Arrows:
- -7 → -9
- -2 → -4
- 0 → -1
- 5 → -4
- Each x maps to only one y → ✔️ Function

> Answer: YES

---

#### 20. Graph: Dots forming an "X" shape
- Points form a cross: symmetric about origin.
- For example, x = 2 has y = 2 and y = -2 → So same x has two y-values → ✘ Fails vertical line test

> Answer: NO

---

✔ Final Answers:

| # | Answer |
|---|--------|
| 1 | NO |
| 2 | YES |
| 3 | YES |
| 4 | YES |
| 5 | YES |
| 6 | YES |
| 7 | NO |
| 8 | NO |
| 9 | YES |
|10 | NO |
|11 | YES |
|12 | YES |
|13 | YES |
|14 | YES |
|15 | YES |
|16 | NO |
|17 | YES |
|18 | YES |
|19 | YES |
|20 | NO |

---

📝 Summary:

- Function if: Each x maps to only one y.
- Not a function if: Any x maps to more than one y.
- Use vertical line test for graphs.

✔ YES: 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 15, 17, 18, 19
✘ NO: 1, 7, 8, 10, 16, 20

---

Let me know if you'd like a printable version or explanation for any specific item!