It looks like you've uploaded an image of a worksheet titled
"Domain and Range from a Graph", which contains several graphs plotted on coordinate grids. The task is likely to determine the
domain and
range for each graph.
Since I can't view images directly, I'll guide you through how to solve this type of problem step by step. If you can describe the graphs or provide details about them (e.g., whether they're lines, parabolas, discrete points, etc.), I can help you find the domain and range for each.
But here’s how to approach it in general:
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🔍 What are Domain and Range?
-
Domain: The set of all possible
x-values (horizontal axis) for which the graph exists.
-
Range: The set of all possible
y-values (vertical axis) for which the graph exists.
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✔ Steps to Find Domain and Range from a Graph:
1.
Look at the horizontal extent of the graph:
- Start from the leftmost point and go to the rightmost point.
- This gives you the
domain.
2.
Look at the vertical extent of the graph:
- Start from the bottommost point and go to the topmost point.
- This gives you the
range.
3.
Use interval notation to express your answer:
- Use parentheses `()` for open endpoints (not included).
- Use brackets `[]` for closed endpoints (included).
- Use infinity symbols `∞` or `-∞` if the graph extends indefinitely.
4.
For discrete points (like dots), list the x-values and y-values separately.
5.
For continuous graphs (like lines or curves), use intervals.
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📌 Example:
Suppose one graph is a line segment from (-2, 1) to (3, 4):
-
Domain: All x-values from -2 to 3 → $[-2, 3]$
-
Range: All y-values from 1 to 4 → $[1, 4]$
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🧩 Common Graph Types:
| Graph Type | Domain | Range |
|------------------|----------------------------|----------------------------|
| Linear line | $(-\infty, \infty)$ | $(-\infty, \infty)$ |
| Parabola opening up/down | $(-\infty, \infty)$ | Depends on vertex |
| Absolute value | $(-\infty, \infty)$ | $[0, \infty)$ |
| Discrete points | List x-values | List y-values |
| Vertical line | Single x-value | All y-values |
| Horizontal line | All x-values | Single y-value |
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🛠️ How You Can Help Me Solve It
Please describe each graph in the worksheet, or tell me:
- What kind of graph is in each box? (e.g., straight line, curve, dots, etc.)
- Coordinates of key points (like endpoints, vertices, intercepts)
- Whether the graph has arrows (indicating continuation)
Then I can give you the
exact domain and range for each one.
Alternatively, if you can copy and paste the description of the graphs or transcribe what's in the image, I’ll solve it fully!
Parent Tip: Review the logic above to help your child master the concept of domain and range graph worksheet.
