The graph presented shows a piecewise-defined function. To determine the domain and range of the function:

Domain:

The domain represents all the possible $x$-values (input values) for which the function is defined. Based on the graph:

• The graph starts at $x = -7$ and ends at $x = 8$, but there is a break between $x = -1$ and $x = 2$.
• So, the domain is $[-7, -1] \cup [2, 8]$.

Thus, the correct answer for the domain is A. $[-7, -1] \text{ and } [2,8]$.

Range:

The range represents all the possible $y$-values (output values) the function can take. Looking at the graph:

• The minimum $y$-value is $-8$ (at the leftmost point) and the maximum is $8$ (at the top-right point).
• The graph covers all $y$-values between $-8$ and $8$.

Thus, the correct answer for the range is D. $[-8, 8]$.

Would you like more detailed explanations or have any questions?

Here are five related questions to expand your understanding:

1. How do you determine if a graph has breaks in its domain?
2. Can a graph have a domain that is all real numbers?
3. How would the domain change if there were vertical asymptotes?
4. What is the difference between the domain and range of a function?
5. How would you identify the range if the graph extended infinitely in the vertical direction?

Tip: When analyzing a graph, always check for any gaps or jumps in the $x$-axis for the domain and the $y$-axis for the range.