Let's analyze the graph to find the correct domain and range of the function.

Domain:

The domain refers to the set of all possible $x$-values where the function is defined. From the graph:

• The function begins at $x = -7$ (a closed circle, so included).
• There is a break at $x = -5$ (an open circle, so not included).
• The function resumes at $x = -2$ (closed circle).
• It continues uninterrupted until $x = 9$ (closed circle).

So, the domain includes two intervals: $[-7, -5) \cup [-2, 9]$.

The correct domain is C: $[-7, -2] \text{ and } [0, 9]$.

Range:

The range refers to the set of all possible $y$-values the function can take. From the graph:

• The lowest point on the graph occurs at $y = -7$ (a closed circle).
• The highest point on the graph occurs at $y = 8$ (a closed circle).
• The function covers all values from $y = -7$ to $y = 8$ without any gaps.

Thus, the correct range is A: $[-7, 8]$.

Would you like further explanation, or do you have any additional questions?

Here are five related questions for practice:

1. What is the significance of an open circle versus a closed circle on a graph?
2. How would the domain change if the break at $x = -5$ were removed?
3. How can we verify the range of a function from its graph?
4. What happens to the domain if the graph extends infinitely in both directions?
5. How do you find the range when there are multiple breaks in a graph?

Tip: Always check for open and closed circles when determining the domain and range from a graph!