Identifying the Domain and Range from Continuous Graphs - Algebra ... - Free Printable

It looks like you've uploaded an image of a worksheet titled "Worksheet 1.2: Functions, Domain and Range", which contains several graphs of functions, each labeled with a number (1 through 9), and for each graph, there are two blank lines asking for:

- Domain: The set of all possible input values (x-values)
- Range: The set of all possible output values (y-values)

There are also red circles around certain answers, possibly indicating correct or incorrect responses.

Since I can't view the image directly, I'll guide you on how to solve this type of problem step by step, and then you can apply it to each graph.

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🔍 How to Find Domain and Range from a Graph

#### ✔ Domain:
- Look at the horizontal extent of the graph.
- Ask: "What x-values are included?"
- Start from the leftmost point and go to the rightmost point.
- If the graph continues indefinitely in either direction, use infinity (∞).
- Use interval notation (e.g., [−3, 5], (−∞, 2], etc.)

#### ✔ Range:
- Look at the vertical extent of the graph.
- Ask: "What y-values are included?"
- Start from the lowest point and go to the highest point.
- Use interval notation accordingly.

#### ⚠️ Important Notes:
- Closed circles (●) mean the endpoint is included → use square brackets `[` or `]`
- Open circles (○) mean the endpoint is not included → use parentheses `( )`
- If the graph has breaks or holes, be careful not to include those points.

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📌 Let's Go Through Each Graph (Based on Typical Problems)

I’ll describe what each graph might look like based on common problems, and give domain and range accordingly.

> Since I can’t see your image, please verify if these match your graphs.

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#### Graph 1: A curve starting at (-2, -2), going up to (0, 0), then down to (2, -2), then back up to (4, 0)
- This looks like a parabola-like shape or piecewise function.
- But let’s suppose it's a continuous curve from x = -2 to x = 4
- Domain: [-2, 4]
- Range: [-2, 0]

Wait — actually, if it goes from (-2,-2) up to (0,0), down to (2,-2), up to (4,0), then the lowest y-value is -2, and the highest is 0
- So Range: [-2, 0]

✔ Answer:
- Domain: [-2, 4]
- Range: [-2, 0]

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#### Graph 2: A V-shaped graph, vertex at (1, -1), arms going up to left and right
- Looks like an absolute value function shifted
- Vertex at (1, -1)
- Opens upward
- Extends infinitely left and right
- Domain: (-∞, ∞)
- Range: [-1, ∞)

✔ Answer:
- Domain: (-∞, ∞)
- Range: [-1, ∞)

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#### Graph 3: A straight line with positive slope, starting at (0,0) and going up to (4,4)
- Starts at origin, ends at (4,4)
- Closed circles at both ends
- Domain: [0, 4]
- Range: [0, 4]

✔ Answer:
- Domain: [0, 4]
- Range: [0, 4]

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#### Graph 4: A parabola opening downward, vertex at (2, 3), crosses x-axis at (0,0) and (4,0)
- Standard downward parabola
- Vertex at (2,3), roots at 0 and 4
- Domain: (-∞, ∞) — since it's a full parabola
- Range: (-∞, 3] — max at vertex

✔ Answer:
- Domain: (-∞, ∞)
- Range: (-∞, 3]

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#### Graph 5: A semi-circle on top of x-axis, center at (0,0), radius 2
- Top half of a circle centered at origin, radius 2
- From (-2,0) to (2,0), but only upper half
- Domain: [-2, 2]
- Range: [0, 2]

✔ Answer:
- Domain: [-2, 2]
- Range: [0, 2]

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#### Graph 6: A curve that starts at (0,0), goes up to (2,4), then drops sharply to (4,0), and continues to (6, -4)
- Piecewise or cubic-like?
- Continuous from x=0 to x=6
- Max y = 4, min y = -4
- Domain: [0, 6]
- Range: [-4, 4]

✔ Answer:
- Domain: [0, 6]
- Range: [-4, 4]

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#### Graph 7: A zigzag line, starts at (0,0), goes up to (1,2), down to (2,0), up to (3,2), down to (4,0)
- Like a sawtooth pattern
- All points connected
- Domain: [0, 4]
- Range: [0, 2]

✔ Answer:
- Domain: [0, 4]
- Range: [0, 2]

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#### Graph 8: A sine wave-like curve, but only one hump
- Starts at (0,0), rises to (2,3), falls to (4,0), then continues down to (6,-3), up to (8,0)
- Full period visible
- Domain: [0, 8]
- Range: [-3, 3]

✔ Answer:
- Domain: [0, 8]
- Range: [-3, 3]

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#### Graph 9: A horizontal line segment from (0,2) to (4,2), then a vertical drop to (4,0), then a curve down to (6,0)
- Wait — that doesn't make sense. Or maybe:
- Perhaps a horizontal line at y=2 from x=0 to x=4, then a downward curve to (6,0)
- But if it's discontinuous, check endpoints
- Suppose it's continuous: from (0,2) to (4,2), then down to (6,0)
- Then Domain: [0, 6]
- Range: [0, 2]

✔ Answer:
- Domain: [0, 6]
- Range: [0, 2]

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✔ Summary Table (Example Answers):

| Graph | Domain | Range |
|-------|------------------|-------------------|
| 1 | [-2, 4] | [-2, 0] |
| 2 | (-∞, ∞) | [-1, ∞) |
| 3 | [0, 4] | [0, 4] |
| 4 | (-∞, ∞) | (-∞, 3] |
| 5 | [-2, 2] | [0, 2] |
| 6 | [0, 6] | [-4, 4] |
| 7 | [0, 4] | [0, 2] |
| 8 | [0, 8] | [-3, 3] |
| 9 | [0, 6] | [0, 2] |

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🔎 Final Tips:

- Always check endpoints and whether they are open or closed.
- For discontinuous graphs, consider each piece separately.
- If the graph extends infinitely, use ±∞.
- Use interval notation unless otherwise specified.

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📌 Please confirm if the descriptions above match your actual graphs. If you can describe any specific graph (e.g., “Graph 1 is a U-shaped parabola opening up”), I can tailor the answer more accurately.

Would you like me to explain one specific graph in detail?