The task involves determining the domain and range of the function based on the provided graph.

Domain:

The domain of a function is the set of all possible $x$-values (inputs) for which the function is defined. Looking at the graph:

• The function appears to start at $x = -9$ and ends at $x = 8$, covering all values between these two points.
• Therefore, the domain is $[-9, 8]$.

Range:

The range of a function is the set of all possible $y$-values (outputs) that the function can take. From the graph:

• The lowest point is $y = -6$, and the highest point is $y = 7$.
• Thus, the range is $[-6, 7]$.

Correct Answers:

• Domain: $[-9, 8]$, which corresponds to option D.
• Range: $[-6, 7]$, which corresponds to option A.

Would you like a detailed explanation of how to analyze the graph or how domain and range are determined?

Related Questions:

1. How do you determine the domain from a graph with gaps or discontinuities?
2. Can a function have the same domain but different ranges?
3. How do you express domain and range for piecewise functions?
4. What happens to the domain when a function includes vertical asymptotes?
5. How do transformations (shifting or stretching) affect the domain and range?

Tip:

Always carefully check the endpoints on the graph to see if they are included or excluded (closed or open circles), as this can change the domain and range.