9 Best Worksheets For Identifying The Domain And Range Of ... - Free Printable

It looks like you've uploaded an image containing 12 graphs arranged in a 4×3 grid, and there are blank lines above and below each graph. Based on the layout and typical math problems involving such graphs, it's likely that the task is to determine whether each graph represents a function or not.

We’ll use the Vertical Line Test to determine this:

> ✔ A graph represents a function if every vertical line intersects the graph at most once.
> ✘ If any vertical line intersects the graph more than once, then it is not a function.

Let’s analyze each graph one by one (row by row, left to right):

---

🔹 Row 1

#### Graph 1: Two vertical line segments (one at x = -2, one at x = 1)
- At x = -2: two points (y = 1 and y = -1) → two outputs for one input
- At x = 1: two points (y = 3 and y = -3)
- ✔ Not a function

#### Graph 2: A piecewise graph with peaks and valleys
- Looks like a continuous graph with multiple turns, but no vertical line crosses it more than once.
- Even though it has peaks and valleys, it passes the vertical line test.
- ✔ Function

#### Graph 3: A wavy curve (like a cubic or higher-degree polynomial)
- Smooth curve, no repeated x-values with multiple y-values.
- ✔ Function

---

🔹 Row 2

#### Graph 4: Horizontal line segment from (-5, 0) to (5, 0), with arrows pointing left and right
- This is a horizontal line (y = 0), extended infinitely.
- Every x-value maps to only one y-value (0).
- ✔ Function

#### Graph 5: A set of discrete points
- Points: (-3, 0), (-2, 0), (0, 3), (1, 0), (2, 3), (4, 0), (0, -3)
- Wait — at x = 0, we have two points: (0, 3) and (0, -3)
- So, same x-value maps to two different y-values
- ✘ Not a function

#### Graph 6: A decreasing curved line from (-5, 2) to (2, -1), with open and closed endpoints
- It's a smooth curve, no vertical overlaps.
- Passes vertical line test.
- ✔ Function

---

🔹 Row 3

#### Graph 7: A circle centered at (1, -1), radius ~2 units
- A circle fails the vertical line test: draw a vertical line through center, it hits two points.
- For example, x = 1 gives two y-values.
- ✘ Not a function

#### Graph 8: A wavy oscillating curve (like a sine wave but more complex)
- No vertical line intersects it more than once.
- Appears to be a continuous function.
- ✔ Function

#### Graph 9: A zigzag line connecting several points
- Starts at (-6, -3), goes up to (-4, 0), down to (-2, -3), up to (0, 0), down to (2, -3), ends at (4, 0)
- All x-values have only one y-value.
- ✔ Function

---

🔹 Row 4

#### Graph 10: A "V" shape, symmetric about y-axis, opening upward
- It looks like |x| shifted down? But wait — it's actually a W-shaped graph?
- Actually, it’s a piecewise linear graph with two V-shapes: left side goes down to (-3, -3), then up; right side goes down to (3, -3), then up.
- But crucially: each x-value has only one y-value
- Even though it's symmetric, no vertical line crosses twice.
- ✔ Function

#### Graph 11: A broken line with open and closed circles
- Points: (-3, -3), (-2, 0), (-1, 1), (0, 0), (1, 1), (2, 0), (3, -1)
- Open circles indicate discontinuities, but still only one output per x
- No x-value repeats
- ✔ Function

#### Graph 12: A triangle-like shape formed by three line segments forming a loop
- This is a closed polygon, forming a triangle
- Draw a vertical line through the middle — it will cross three times (once per side)
- So, multiple y-values for one x-value
- ✘ Not a function

---

✔ Final Answers (Function or Not?)

Let’s list them in order (left to right, top to bottom):

1. Not a function → fails vertical line test (multiple y-values at x = -2, x = 1)
2. Function
3. Function
4. Function
5. Not a function → x = 0 has two y-values
6. Function
7. Not a function → circle
8. Function
9. Function
10. Function
11. Function
12. Not a function → triangle fails vertical line test

---

✔ Summary Table:

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

---

📝 Instructions for Filling in Blanks:

If the blanks are meant for writing “Function” or “Not a Function”, write accordingly:

```
Graph 1: Not a Function
Graph 2: Function
Graph 3: Function
Graph 4: Function
Graph 5: Not a Function
Graph 6: Function
Graph 7: Not a Function
Graph 8: Function
Graph 9: Function
Graph 10: Function
Graph 11: Function
Graph 12: Not a Function
```

Let me know if you need explanations for specific graphs or if the task was something else (e.g., domain/range, even/odd, etc.).