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what is the greater then 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 all possible \( x \)-values (horizontal axis) that the function covers. From the graph:

- The line segment starts at a point where the \( x \)-coordinate is negative and extends to a point where the \( x \)-coordinate is positive.
- It appears the \( x \)-values range from approximately \( x = -5 \) to \( x = 3 \).

Thus, the domain is \( -5 \leq x \leq 3 \).

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

- The \( y \)-values seem to start from a value near \( y = -2 \) and extend to a value around \( y = 4 \).

Thus, the range is \( -2 \leq y \leq 4 \).

### Greater Than or Less Than:
Since the graph shows a line segment (indicating that the endpoints are included):

- The domain is \( -5 \leq x \leq 3 \).
- The range is \( -2 \leq y \leq 4 \).

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. How do you identify the domain and range of a function from its graph?
2. What changes would occur in the domain and range if the line were extended beyond the endpoints?
3. How does the slope of the line affect the domain and range?
4. Can a line segment have a domain and range that are not intervals?
5. How would the domain and range differ if the graph represented a vertical line?

**Tip:** Always remember that the domain relates to the \( x \)-values, while the range relates to the \( y \)-values of a function.

Understand how to determine the domain and range of a function from its graph. This detailed explanation covers the concepts of domain, range, intervals, and includes examples to illustrate the process. Suitable for students in Grades 9-12.

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