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).