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 vertical overlaps.
- ✔ Function

---

🔹 Row 2

#### Graph 4: A horizontal line with arrows pointing left and right
- This is the x-axis, extended infinitely.
- Every x-value has exactly one y-value (y = 0).
- ✔ Function

#### Graph 5: A set of discrete points
- Points at: (-3, -1), (-2, 0), (0, 3), (2, 3), (4, 2), (1, -2)
- No two points share the same x-coordinate.
- ✔ Function (discrete)

#### Graph 6: A curved line from left to right, decreasing
- It’s a smooth curve (possibly a square root or rational function), but no vertical line hits it twice.
- ✔ Function

---

🔹 Row 3

#### Graph 7: A circle centered at origin
- A circle fails the vertical line test (e.g., at x = 0, two y-values: y = ±2)
- ✘ Not a function

#### Graph 8: A wavy periodic-like graph (oscillating up and down)
- Multiple peaks and troughs, but still only one y-value per x.
- ✔ Function

#### Graph 9: A zigzag line (piecewise linear)
- Appears to be a V-shaped pattern with steps.
- Each x has only one y-value.
- ✔ Function

---

🔹 Row 4

#### Graph 10: A "W"-shaped graph (V-shape mirrored)
- Looks like a series of V’s, but still, each x has only one y-value.
- ✔ Function

#### Graph 11: A graph with open and closed circles (discontinuities)
- Has jumps and holes, but no vertical line intersects it more than once.
- ✔ Function

#### Graph 12: A triangle shape (connected lines forming a triangle)
- This is a closed loop — for example, at x = 1, there are two y-values (top and bottom of triangle).
- Vertical line through center hits two points.
- ✘ Not a function

---

✔ Final Answers (Row by Row):

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

---

📝 Summary:

You should write "Yes" or "No" in the blank lines above or below each graph depending on whether it represents a function.

So the correct answers are:

```
Graph 1: No
Graph 2: Yes
Graph 3: Yes
Graph 4: Yes
Graph 5: Yes
Graph 6: Yes
Graph 7: No
Graph 8: Yes
Graph 9: Yes
Graph 10: Yes
Graph 11: Yes
Graph 12: No
```

Let me know if you need help labeling them directly or if the task was different (e.g., domain/range, symmetry, etc.).