To analyze the graph and determine the domain and range, let's break it down:

Domain

• The domain refers to all possible $x$-values for which the function is defined.
• From the graph, we can see the function starts at $x = -7$ and ends at $x = 8$, but there seems to be a gap in the graph between $x = -1$ and $x = 2$.
• Therefore, the domain consists of two intervals: $[-7, -1]$ and $[2, 8]$.

The correct choice for the domain is C: $[-7, -1]$ and $[2, 8]$.

Range

• The range refers to all possible $y$-values the function can take.
• Looking at the graph, the lowest point of the function is at $y = -6$ and the highest is at $y = 8$.
• This means the range of the function is from $y = -6$ to $y = 8$, inclusive.

The correct choice for the range is C: $[-6, 8]$.

Would you like further clarification on any of these points?

Related Questions:

1. What is the difference between domain and range?
2. How do you determine if a function has gaps in its domain?
3. What types of functions typically have restricted domains?
4. How can you determine the range of a function from a graph?
5. Can a function have the same domain but a different range?

Tip:

Always check for discontinuities or gaps in the graph when determining the domain of a function.