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To determine the correct inequalities describing the domain and range of the given graph of the linear function \( g \), let’s analyze the graph step-by-step:

### Domain Analysis:
- The domain represents all possible \( x \)-values of the function.
- From the graph, the line starts at the point \((-7, -4)\) and ends at the point \((6, 5)\).
- Therefore, the domain of the function is \(-7 \leq x \leq 6\).

### Range Analysis:
- The range represents all possible \( y \)-values of the function.
- From the graph, the lowest point is \((-7, -4)\) and the highest point is \((6, 5)\).
- Thus, the range of the function is \(-4 \leq g(x) \leq 5\).

### Correct Answer:
- The inequalities that best describe the domain and range are:
  - **Domain**: \(-7 \leq x \leq 6\)
  - **Range**: \(-4 \leq g(x) \leq 5\)

This matches the selected answer: 
- **Domain: \(-7 \leq x \leq 6\)**
- **Range: \(-4 \leq g(x) \leq 5\)**

Would you like further details or have any questions?

### Related Questions:
1. How do you determine the domain and range from a graph?
2. What is the importance of understanding the domain and range of a function?
3. How can you express domain and range using interval notation?
4. What other types of functions have specific domains and ranges?
5. How does the slope of a line affect the range of a function?

### Tip:
Always pay close attention to the endpoints of a graph when determining the domain and range, especially whether the points are included or excluded (open or closed circles).

Which inequalities best describe the domain and range of the part of the linear function g graphed on the grid?

Analyze the domain and range of a part of the linear function g from the graph provided. Learn to identify the correct inequalities describing the domain and range for students in Grades 7-10.

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