It looks like you've uploaded an image of a worksheet titled
"Domain and Range of Graphs", 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) that the graph covers.
---
✔ 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.
- Use
interval notation or
inequalities.
2.
Look at the vertical extent of the graph:
- Start from the lowest point and go to the highest point.
- This gives you the
range.
3.
Check if the graph includes endpoints:
- A
closed circle means the endpoint is included.
- An
open circle means it's not included.
4.
For continuous graphs (like lines or curves):
- Use intervals: e.g., $[-2, 5]$, $(-\infty, 3)$, etc.
5.
For discrete points:
- List the x-values and y-values separately.
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📌 Example (Hypothetical)
Suppose one graph is a straight line from $(-3, 1)$ to $(4, 6)$, with closed circles at both ends.
-
Domain: All x-values from $-3$ to $4$ → $[-3, 4]$
-
Range: All y-values from $1$ to $6$ → $[1, 6]$
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🧩 Common Graph Types
| Graph Type | Typical Domain | Typical Range |
|------------------|-----------------------------|-----------------------------|
| Line | $(-\infty, \infty)$ | $(-\infty, \infty)$ |
| Parabola (up) | $(-\infty, \infty)$ | $[k, \infty)$ (k = vertex y) |
| Parabola (down) | $(-\infty, \infty)$ | $(-\infty, k]$ |
| Vertical line | Single value (e.g., $x=2$) | $(-\infty, \infty)$ |
| Horizontal line | $(-\infty, \infty)$ | Single value (e.g., $y=3$) |
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💡 Tips
- If the graph goes off the grid, assume it continues unless restricted.
- For piecewise or broken graphs, analyze each segment.
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👉
Please describe the graphs in your worksheet (e.g., "Graph 1 is a line from (-2,0) to (2,4)", or "Graph 3 is a downward parabola with vertex at (0,3)"), and I’ll help you fill in the domain and range for each!
Alternatively, if you can list the characteristics of each graph, I can walk you through solving them one by one.
Parent Tip: Review the logic above to help your child master the concept of domain and range of a graph worksheet.
