The graph provided depicts a piecewise function that consists of two linear segments. Let's determine the domain and range in interval notation.

Domain:

The domain is the set of all possible $x$-values for which the function is defined.

• The first segment starts at $x = -8$ and continues to $x = 2$.
• The second segment starts at $x = 2$ and extends indefinitely to the right.

The function is defined for all $x$-values from $-8$ to infinity, with a transition at $x = 2$.

Thus, the domain in interval notation is: $\text{Domain} = [-8, \infty)$

Range:

The range is the set of all possible $y$-values that the function takes.

• The first segment begins at $y = -8$ (when $x = -8$) and ends at $y = -3$ (when $x = 2$).
• The second segment starts at $y = -3$ (when $x = 2$) and increases indefinitely.

Therefore, the function covers all $y$-values from $-8$ to infinity.

Thus, the range in interval notation is: $\text{Range} = [-8, \infty)$

Summary:

• Domain: $[-8, \infty)$
• Range: $[-8, \infty)$

Would you like to go over any specific details, or do you have any further questions?

Here are five related questions that could be useful:

1. How would the domain and range change if the function had a vertical asymptote?
2. What would the domain and range look like if the graph included a hole or discontinuity?
3. How do you find the domain and range for a quadratic function?
4. What happens to the range if the function is reflected across the x-axis?
5. How can you determine if a function is one-to-one based on its graph?

Tip: When working with piecewise functions, always check each segment individually to determine the overall domain and range.