Describing Domain and Range from Graphs | Math Lesson & Worksheet by Mr. Slope Guy - Free Printable

It looks like you've uploaded an image containing a worksheet with 12 graphs, each labeled with a number (1 through 12), and for each graph, you're asked to determine the domain and range.

Since I can't view images directly, I’ll need you to describe the graphs or provide details about them. However, I can guide you through how to solve such problems step by step.

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🔍 How to Find Domain and Range from a Graph:

#### ✔ Domain: The set of all possible x-values (horizontal axis) for which the function is defined.
- Look at the leftmost and rightmost points on the graph.
- If it's a continuous line or curve, include all x-values between those points.
- Use interval notation (e.g., [a, b], (-∞, ∞), etc.).

#### ✔ Range: The set of all possible y-values (vertical axis) that the function takes.
- Look at the lowest and highest points on the graph.
- Again, use interval notation.

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📌 General Rules:

- Closed circles = included in domain/range → use square brackets `[ ]`
- Open circles = not included → use parentheses `( )`
- Lines extending infinitely → use `±∞` with parentheses

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Let’s go through some common types of graphs:

| Graph Type | Domain | Range |
|-----------|--------|-------|
| Straight line (e.g., y = x) | (-∞, ∞) | (-∞, ∞) |
| Parabola opening up (e.g., y = x²) | (-∞, ∞) | [0, ∞) |
| Circle | [a - r, a + r] | [b - r, b + r] |
| Absolute value (V-shape) | (-∞, ∞) | [0, ∞) |
| Step function | depends on segments | depends on output values |
| Trigonometric wave (like sine) | (-∞, ∞) | [-1, 1] if amplitude is 1 |

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Example: Suppose one graph is a parabola opening upward with vertex at (0, -2)

- Domain: All real numbers → (-∞, ∞)
- Range: From y = -2 upward → [-2, ∞)

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Now, let’s suppose your worksheet includes these kinds of graphs:

1. Graph 1: A downward-opening parabola
→ Domain: (-∞, ∞), Range: (-∞, max]

2. Graph 2: A V-shaped absolute value graph
→ Domain: (-∞, ∞), Range: [min, ∞)

3. Graph 3: A circle centered at origin, radius 3
→ Domain: [-3, 3], Range: [-3, 3]

4. Graph 4: A horizontal line segment from x = 1 to x = 5 at y = 2
→ Domain: [1, 5], Range: {2} (single value)

5. Graph 5: A sine wave over a finite interval
→ Domain: [a, b], Range: [-1, 1] (if amplitude is 1)

6. Graph 6: A piecewise function with jumps
→ Carefully identify all x-values covered and y-values reached

7. Graph 7: A semicircle (top half of circle)
→ Domain: [a, b], Range: [c, d] (depending on center and radius)

8. Graph 8: A vertical line? → Not a function! But still, domain is single x-value, range is full y-interval.

9. Graph 9: A zigzag line (like a sawtooth)
→ Domain: [start, end], Range: [min, max]

10. Graph 10: A curved exponential-like graph
→ Domain: (-∞, ∞), Range: (0, ∞) — if it's exponential growth

11. Graph 11: A periodic oscillation (like cosine)
→ Domain: (-∞, ∞), Range: [min, max]

12. Graph 12: A slanted line with open circle at endpoint
→ Domain: (a, b], Range: (c, d] — depending on endpoints

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❗ Important Notes:

- If a graph has open circles, those points are not included.
- If a graph doesn’t extend to infinity, limit domain/range accordingly.
- For non-functions (like circles), domain and range are still defined but the graph fails the vertical line test.

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🛠️ What You Can Do:

Please describe each of the 12 graphs briefly (e.g., “Graph 1 is a downward parabola with vertex at (0, 4)” or “Graph 5 is a sine wave from x = 0 to x = 2π”), and I’ll help you fill out the domain and range for each.

Alternatively, if you can transcribe the graphs’ descriptions or sketch them in text, I can give exact answers.

Let me know how you'd like to proceed!