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what would be the greater than or less than of domain and range

To determine the domain and range of the function based on the graph provided:

### Domain:
The domain refers to the set of all possible \( x \)-values (horizontal axis) that the function covers. From the graph:

- The line segment starts at a point with an \( x \)-coordinate less than 0 and extends to a point where the \( x \)-coordinate is positive.
- It appears the \( x \)-values range from approximately \( x = -2 \) to \( x = 3 \).

Thus, the domain is \( -2 \leq x \leq 3 \).

### Range:
The range refers to the set of all possible \( y \)-values (vertical axis) that the function covers. From the graph:

- The \( y \)-values seem to start from a value less than 2 and extend to a value around 5.
  
Thus, the range is \( 2 \leq y \leq 5 \).

### Greater Than or Less Than:
Since the graph shows a line segment (not an open-ended line or curve), the domain and range include the endpoints.

- The domain is given as \( -2 \leq x \leq 3 \).
- The range is given as \( 2 \leq y \leq 5 \).

Both the domain and range use "greater than or equal to" and "less than or equal to" (≤ and ≥) since the points at the endpoints are included.

Would you like further details or have any questions? Here are some related questions:

1. What is the difference between domain and range?
2. How would the domain and range change if the line was extended infinitely in both directions?
3. How do you determine the domain and range for more complex graphs, such as parabolas or circles?
4. Can domain and range be represented using interval notation?
5. How do you graph a function if only the domain or range is provided?

**Tip:** Remember, the domain and range can also be visualized as the "shadow" that the graph casts on the \( x \)-axis (domain) and the \( y \)-axis (range).

Learn how to determine the domain and range of a function with detailed explanations and examples. This guide covers the mathematical concepts of functions, graphing, domain, and range using real-world examples. Suitable for high school students.

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