Algebra 1 Worksheets | Domain and Range Worksheets - Free Printable

Let's solve each of the 8 problems on the worksheet step by step. For each graph, we will determine:

1. Domain: The set of all possible x-values (horizontal extent).
2. Range: The set of all possible y-values (vertical extent).
3. Function?: Whether the graph represents a function (use the Vertical Line Test — if any vertical line intersects the graph more than once, it is not a function).

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1) Graph 1

- Graph Description: A single curve from (0, 4) to (2, 0), decreasing, with a solid dot at (0, 4) and an open circle at (2, 0).
- Domain: x-values from 0 to 2 → [0, 2)
- Range: y-values from 0 to 4 → [0, 4]
- Function?: Yes – passes vertical line test.
- ✔ Answer:
- Domain: [0, 2)
- Range: [0, 4]
- Function: Yes

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2) Graph 2

- Graph Description: A downward-opening parabola arc from (-3, 0) to (3, 0), peaking at (0, 3). Solid dots at endpoints.
- Domain: x-values from -3 to 3 → [-3, 3]
- Range: y-values from 0 to 3 → [0, 3]
- Function?: Yes – every x has only one y-value.
- ✔ Answer:
- Domain: [-3, 3]
- Range: [0, 3]
- Function: Yes

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3) Graph 3

- Graph Description: A wavy curve from (-3, -2) to (3, 2), with open circles at both ends. It goes up and down multiple times.
- Domain: x-values from -3 to 3 → (-3, 3)
- Range: y-values from -2 to 2 → (-2, 2)
- Function?: Yes – no vertical line crosses it more than once.
- ✔ Answer:
- Domain: (-3, 3)
- Range: (-2, 2)
- Function: Yes

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4) Graph 4

- Graph Description: Two separate parts: left side from (-3, -1) to (-1, 1), right side from (-1, 1) to (1, -1). Open circles at (-3, -1) and (1, -1), solid dot at (-1, 1).
- Domain: x-values from -3 to 1, but two segments: [-3, -1] and [-1, 1] → [-3, 1]
- Range: y-values from -1 to 1 → [-1, 1]
- Function?: No! At x = -1, there are two y-values: one from left segment and one from right (the top point is shared). But since it’s a single point, actually wait — let’s check:
- At x = -1, the point (-1, 1) is solid, and it connects both parts.
- However, the graph appears to have a "corner" or "kink" at (-1, 1), but still only one output per input.
- Wait — actually, looking closely: the left part ends at (-1, 1) (solid), and the right part starts at (-1, 1) (solid). So same point. That's fine.
- But does it pass the vertical line test? Yes — each x has only one y.
- BUT: look at the shape — it's like a sideways "V" or two lines meeting at (-1,1). Still, it's one value per x.
- Actually, this is a function.
- ✔ Answer:
- Domain: [-3, 1]
- Range: [-1, 1]
- Function: Yes

Wait — re-examining: the left segment goes from (-3, -1) to (-1, 1), and the right segment goes from (-1, 1) to (1, -1). So for x in [-3, -1], y increases; for x in [-1, 1], y decreases. At x = -1, only one point: (-1, 1). So yes, it's a function.

✔ Final Answer:
- Domain: [-3, 1]
- Range: [-1, 1]
- Function: Yes

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5) Graph 5

- Graph Description: A line segment from (-3, 2) to (0, -1), then another from (0, -1) to (1, -1). Open circle at (-3, 2), solid at (0, -1), and solid at (1, -1).
- Domain: x-values from -3 to 1 → (-3, 1]
- Range: y-values from -1 to 2 → [-1, 2)
- Function?: Yes – each x has only one y.
- ✔ Answer:
- Domain: (-3, 1]
- Range: [-1, 2)
- Function: Yes

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6) Graph 6

- Graph Description: A straight line starting at (-3, -2) going upward through origin to (3, 4). Solid dots at both ends.
- Domain: x-values from -3 to 3 → [-3, 3]
- Range: y-values from -2 to 4 → [-2, 4]
- Function?: Yes – straight line, passes vertical line test.
- ✔ Answer:
- Domain: [-3, 3]
- Range: [-2, 4]
- Function: Yes

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7) Graph 7

- Graph Description: A line segment from (-3, 2) to (0, -2). Open circle at (-3, 2), solid at (0, -2).
- Domain: x-values from -3 to 0 → (-3, 0]
- Range: y-values from -2 to 2 → [-2, 2)
- Function?: Yes – straight line, one y per x.
- ✔ Answer:
- Domain: (-3, 0]
- Range: [-2, 2)
- Function: Yes

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8) Graph 8

- Graph Description: A curved graph that starts at (-3, 1), goes down to (-1, -3), then up to (3, 2). Open circles at (-3, 1) and (3, 2), solid dot at (-1, -3).
- Domain: x-values from -3 to 3 → (-3, 3)
- Range: y-values from -3 to 2 → [-3, 2)
- Function?: Let's check vertical line test.
- The graph appears to be a continuous curve, but looks like a parabola-like shape, opening upwards.
- But wait — it dips down to (-1, -3) and then rises. Is it one-to-one?
- Actually, no: if you draw a vertical line at x = 0, it hits the graph once. But what about other points?
- Actually, this seems to be a function — it's a smooth curve with no backtracking vertically.
- But let’s think: from (-3,1) to (-1,-3) to (3,2). It’s not symmetric, but it's monotonic in parts.
- Does any vertical line cross twice? No — it’s a single path.
- So it is a function.
- ✔ Answer:
- Domain: (-3, 3)
- Range: [-3, 2)
- Function: Yes

Wait — double-check: the graph starts at (-3,1) (open), goes down to (-1,-3) (solid), then up to (3,2) (open). This is a U-shaped curve, but shifted. Since it's a single-valued curve (no loops), it is a function.

Yes, it passes the vertical line test.

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✔ Final Answers Summary:

| # | Domain | Range | Function? |
|---|------------------|------------------|-----------|
| 1 | [0, 2) | [0, 4] | Yes |
| 2 | [-3, 3] | [0, 3] | Yes |
| 3 | (-3, 3) | (-2, 2) | Yes |
| 4 | [-3, 1] | [-1, 1] | Yes |
| 5 | (-3, 1] | [-1, 2) | Yes |
| 6 | [-3, 3] | [-2, 4] | Yes |
| 7 | (-3, 0] | [-2, 2) | Yes |
| 8 | (-3, 3) | [-3, 2) | Yes |

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📝 Notes:

- Open circle means the endpoint is not included → use parentheses.
- Closed/solid dot means the endpoint is included → use brackets.
- Domain: All x-values covered.
- Range: All y-values covered.
- Function: Use Vertical Line Test — if any vertical line crosses the graph more than once → Not a function.

In this case, all graphs represent functions.

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✔ Final Answer Key (for student):

1)
- Domain: [0, 2)
- Range: [0, 4]
- Function: Yes

2)
- Domain: [-3, 3]
- Range: [0, 3]
- Function: Yes

3)
- Domain: (-3, 3)
- Range: (-2, 2)
- Function: Yes

4)
- Domain: [-3, 1]
- Range: [-1, 1]
- Function: Yes

5)
- Domain: (-3, 1]
- Range: [-1, 2)
- Function: Yes

6)
- Domain: [-3, 3]
- Range: [-2, 4]
- Function: Yes

7)
- Domain: (-3, 0]
- Range: [-2, 2)
- Function: Yes

8)
- Domain: (-3, 3)
- Range: [-3, 2)
- Function: Yes

Let me know if you'd like a printable version or explanations with visual cues!