To solve this problem, let’s first define the domain and range of a graphed function:

1. Domain: The set of all possible input values (x-values) for which the function is defined.
2. Range: The set of all possible output values (y-values, or g(x)) for the function.

For each option, the inequalities describe the domain and range.

• Domain: Refers to the interval of $x$-values (from left to right on the graph).
• Range: Refers to the interval of $g(x)$ or $y$-values (from bottom to top on the graph).

Let’s break down the options:

A. Domain: $-7 < x < 6$, Range: $-4 < g(x) < 5$

• The inequalities in the domain and range are strict, meaning that the function does not include the endpoints.

B. Domain: $-7 \leq x \leq 6$, Range: $-4 \leq g(x) \leq 5$

• The inequalities are inclusive, meaning the function includes the endpoints of the domain and range.

C. Domain: $-4 \leq x \leq 5$, Range: $-7 \leq g(x) \leq 6$

• The domain and range appear reversed when compared to the rest.

D. Domain: $-4 < x < 5$, Range: $-7 < g(x) < 6$

• Both domain and range use strict inequalities, and the intervals are reversed.

Choosing the Correct Answer

Without the graph, option B seems the most reasonable as it includes the endpoint values, which is common in such questions. If the graph shows the function defined at those boundary points, then B is the best choice.

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Let me know if you'd like further details or have any questions! Here are 5 related questions to explore:

1. How do you find the domain and range of a function from a graph?
2. What is the difference between strict and inclusive inequalities?
3. How do you find the domain and range of a linear function algebraically?
4. What is the significance of endpoint inclusion in a domain or range?
5. How would you represent a function with an infinite domain or range?

Tip: Always check if the endpoints are included in the graph to decide between strict (<) and inclusive (≤) inequalities.