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To determine the domain of the function \( h(x) \) from the graph, we need to find the range of values of \( x \) for which the function is defined.

Looking at the graph:

- The function starts at \( x = -5 \) (there is a filled circle at \( (-5, 2) \)).
- The function ends at \( x = 7 \) (another filled circle at \( (7, -1) \)).

So, the domain of \( h(x) \) is all \( x \)-values from \( -5 \) to \( 7 \), inclusive. This can be written as:

\[
-5 \leq x \leq 7
\]

Therefore, the correct option is **B: \(-5 \leq x \leq 7\)**.

Would you like more details or have any other questions?

Here are five related questions to deepen understanding:
1. How do you determine the range of a function from a graph?
2. What does it mean when a point on the graph is a closed (filled) circle?
3. What is the difference between the domain and the range of a function?
4. How would the domain change if there were an open circle at \( x = 7 \)?
5. How can you find the domain of more complex functions, such as rational functions?

**Tip**: The domain represents all the possible input values (or \( x \)-values) that will result in a valid output for the function. Always check for any restrictions, such as divisions by zero or square roots of negative numbers.

Learn how to determine the domain of the function h(x) from a graph. This problem involves analyzing the function's x-values to find the range where the function is defined. Suitable for students in Grades 7-10.

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