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To determine the domain and range restrictions for the given line \( y = -x - 2 \) between points \( A \) and \( B \), we need to examine the coordinates of these points on the graph.

### Step 1: Identify the coordinates of points \( A \) and \( B \)
From the graph:
- Point \( A \) is located at approximately \( (-9, 7) \).
- Point \( B \) is located at approximately \( (5, -7) \).

### Step 2: Find the domain restriction
The domain corresponds to the possible values of \( x \) between points \( A \) and \( B \). Since \( A \) has an \( x \)-coordinate of \( -9 \) and \( B \) has an \( x \)-coordinate of \( 5 \), the domain restriction is:

\[
-9 \leq x \leq 5
\]

### Step 3: Find the range restriction
The range corresponds to the possible values of \( y \) between points \( A \) and \( B \). Since \( A \) has a \( y \)-coordinate of \( 7 \) and \( B \) has a \( y \)-coordinate of \( -7 \), the range restriction is:

\[
-7 \leq y \leq 7
\]

### Final answer:
- **Domain restriction:** \( -9 \leq x \leq 5 \)
- **Range restriction:** \( -7 \leq y \leq 7 \)

Would you like further details or clarification? Here are some related questions to explore:

1. How do we calculate the slope of the line \( y = -x - 2 \) from its equation?
2. What are other methods to restrict the domain and range of a function?
3. How do vertical and horizontal shifts affect the domain and range of a line?
4. Can the domain and range be written in interval notation?
5. What changes would occur if the line were translated or rotated?

**Tip:** Always check the coordinates of points carefully when finding domain and range restrictions in graphs!

Determine the domain and range of y = -x - 2 to restrict the graph from point A to point B.

Explore how to determine the domain and range restrictions for the linear function y = -x - 2. This problem uses the points A (-9, 7) and B (5, -7) on the graph to find the restricted domain and range. Suitable for students in Grades 8-10.

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