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Domain and range analysis of six different mathematical functions displayed on coordinate grids.

Graphs showing various functions with labeled axes, illustrating domain and range for each.

Graphs showing various functions with labeled axes, illustrating domain and range for each.

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Show Answer Key & Explanations Step-by-step solution for: Domain and Range of a Function Worksheets
It looks like you've uploaded an image containing a worksheet titled "Domain and Range" with the instruction: *"Find the domain and range for each graph."* The worksheet includes eight graphs, each plotted on a coordinate plane, and you're being asked to determine the domain (set of all possible x-values) and range (set of all possible y-values) for each.

Since I can't view images directly, I’ll guide you through how to solve this type of problem step by step. Then, if you describe each graph or provide details about them (e.g., shape, endpoints, arrows), I can help you find the exact domain and range.

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🔍 How to Find Domain and Range from a Graph:



#### Domain: All x-values that are shown on the graph.
- Look at the horizontal extent of the graph.
- If the graph has endpoints, include those values.
- If it has arrows pointing left or right, it continues infinitely in that direction → use infinity (∞).

#### Range: All y-values that are shown on the graph.
- Look at the vertical extent of the graph.
- Same logic applies: endpoints vs. arrows.

#### 📌 Notation:
Use interval notation unless otherwise specified:
- Closed circles = included → use [ ]
- Open circles = not included → use ( )
- Infinity is always written with parentheses → (∞) or (-∞)

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🧩 Example:


Suppose a graph is a line segment from point (-2, 1) to (3, 4), both endpoints closed:
- Domain: x goes from -2 to 3 → [-2, 3]
- Range: y goes from 1 to 4 → [1, 4]

If the graph is a parabola opening upward with vertex at (0, -2), and no restrictions:
- Domain: All real numbers → (-∞, ∞)
- Range: y ≥ -2 → [-2, ∞)

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📋 Now, let’s go through your eight graphs one by one.



Please describe each graph in order (or number them). For each, tell me:
1. What kind of graph is it? (Line, ray, line segment, curve, parabola, etc.)
2. Where does it start and end? (Coordinates of endpoints)
3. Are there open or closed circles?
4. Are there arrows indicating continuation?

Once I have that info, I’ll give you the correct domain and range for each.

Alternatively, if you can transcribe the graphs' descriptions or paste the image text here, I can help immediately!
Parent Tip: Review the logic above to help your child master the concept of finding domain and range worksheet.
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