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—likely for labeling or classification. Based on the context, this appears to be a "function or not a function" identification exercise, where you're supposed to determine whether each graph represents a function.

Let’s go through each graph one by one and apply the Vertical Line Test:

> ✔ Vertical Line Test: A graph represents a function if no vertical line intersects the graph more than once.
> If any vertical line crosses the graph at more than one point → not a function.

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🔹 Graph 1 (Top-left)

- Two vertical segments: one from (−1, −3) to (−1, 0), and another from (1, 0) to (1, 3).
- At x = −1, there are multiple y-values → fails vertical line test
- ✘ Not a function

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🔹 Graph 2 (Top-middle)

- A piecewise graph with peaks and valleys.
- It's a continuous curve that goes up and down but never has two points at the same x-value.
- Every vertical line hits it at most once.
- ✔ Function

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🔹 Graph 3 (Top-right)

- A wavy curve going up and down, resembling a cubic or higher-degree polynomial.
- Smooth curve with no repeated x-values.
- ✔ Function

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🔹 Graph 4 (Row 2, Left)

- A horizontal line segment at y = 1, extending left and right.
- This is part of a horizontal line, which is a constant function.
- ✔ Function

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🔹 Graph 5 (Row 2, Middle)

- A set of discrete points:
- (−2, 0), (−1, 0), (0, 3), (1, 0), (2, 0), (3, 1), (4, 0), (0, −2)
- Wait — two points at x = 0: (0, 3) and (0, −2)
- So at x = 0, two different y-values → fails vertical line test
- ✘ Not a function

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🔹 Graph 6 (Row 2, Right)

- A decreasing curved line from left to right, starting at (−4, 2) and ending at (1, −1).
- No vertical line intersects it more than once.
- ✔ Function

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🔹 Graph 7 (Row 3, Left)

- A circle centered at (1, −1), radius ≈ 2 units.
- A circle fails the vertical line test — e.g., at x = 1, there are two y-values (top and bottom of circle).
- ✘ Not a function

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🔹 Graph 8 (Row 3, Middle)

- A wavy periodic-like curve, similar to sine wave, but with sharp turns.
- Still, it passes the vertical line test — each x has only one y.
- ✔ Function

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🔹 Graph 9 (Row 3, Right)

- A zigzag path made of line segments.
- Looks like a "V" shape mirrored and connected.
- But notice: at some x-values (e.g., x = 0), there are two y-values?
- Let's check: from the graph, it seems to go from (−4, −3) → (−2, 1) → (0, 3) → (2, 1) → (4, 3), then down to (−2, −3) → (0, −3)?
- Wait — actually, it's two separate paths? Or is it a single continuous path?

Looking closely: it starts at (−4, −3), goes up to (−2, 1), then to (0, 3), then to (2, 1), then to (4, 3). Then it goes down from (−2, −3) to (0, −3), etc.

Wait — there are two different y-values at x = −2: one at y = 1 and one at y = −3? That would be two points at x = −2.

But look: the top path is from (−4, −3) → (−2, 1) → (0, 3) → (2, 1) → (4, 3)
The bottom path is from (−2, −3) → (0, −3) → (2, −3) → (4, −3)

So both paths have points at x = −2: (−2, 1) and (−2, −3) → same x, different y
→ ✘ Not a function

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🔹 Graph 10 (Row 4, Left)

- A V-shaped graph, symmetric about y-axis.
- Looks like |x| but shifted down.
- However, it's continuous and each x has one y.
- ✔ Function

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🔹 Graph 11 (Row 4, Middle)

- A piecewise graph with open and closed circles.
- Open circle at (−1, 1), closed at (−1, 0)? Wait — let's analyze:
- From x = −3 to x = −1: increasing from (−3, −3) to (−1, 0) — closed dot at (−1, 0)
- Then from x = −1 to x = 1: a horizontal line from (−1, 1) to (1, 1) — but (−1, 1) is open, so not included
- Then from x = 1 to x = 3: decreasing from (1, 1) to (3, −1), closed at (1, 1), open at (3, −1)
- Now, at x = −1: we have a closed dot at (−1, 0) and an open dot at (−1, 1) → so only one value defined: y = 0
- At x = 1: closed dot at (1, 1), so only one value
- No x has two y-values → ✔ Function

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🔹 Graph 12 (Row 4, Right)

- A triangle-shaped figure: connects (−2, −1) → (0, 1) → (2, −1) → back to (−2, −1)
- This forms a triangle, but it's a closed loop.
- For example, at x = 0: there are two y-values: y = 1 and y = −1? Wait — the line from (−2, −1) to (0, 1), then (0, 1) to (2, −1), and (2, −1) back to (−2, −1)
- The bottom side from (2, −1) to (−2, −1) is horizontal.
- So at x = 0: we have:
- Point (0, 1) — top vertex
- Also on the bottom line: (0, −1)
- So two points at x = 0: (0, 1) and (0, −1) → fails vertical line test
- ✘ Not a function

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✔ Final Answers (Function or Not?)

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

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📝 Summary

You can write the answers in the blanks as:

```
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: Not a function
Graph 10: Function
Graph 11: Function
Graph 12: Not a function
```

Or simply mark each blank with "Function" or "Not a function" accordingly.

Let me know if you'd like to classify them further (e.g., linear, quadratic, etc.) or if there was a specific question attached!