From the image, we can observe a graph with two distinct points: the highest point (y = 4) and the lowest point (y = -5). The graph covers values of $x$ from -5 to 4 and values of $y$ from -5 to 4 as well. Let's analyze the options provided to find the correct set-builder notation for the domain and range.

1. Domain: The graph exists between $x = -5$ and $x = 4$, meaning the domain is all $x$-values from -5 to 4. $\text{Domain: } \{x \mid -5 \leq x \leq 4\}$

2. Range: The graph extends vertically from $y = -5$ to $y = 4$, so the range includes all $y$-values from -5 to 4. $\text{Range: } \{y \mid -5 \leq y \leq 4\}$

Thus, the correct answer is the option that reflects:

• Domain: $\{x \mid -5 \leq x \leq 4\}$
• Range: $\{y \mid -5 \leq y \leq 4\}$

This matches option 2 in your image.

Would you like more details on how the domain and range were derived?

Here are five related questions:

1. How would the domain and range change if the graph were shifted horizontally or vertically?
2. What is the difference between set-builder notation and interval notation?
3. How can you identify the domain and range of more complex graphs like parabolas?
4. What is the domain and range of the absolute value function?
5. How does the concept of domain and range apply to real-world situations?

Tip: The domain represents all possible input values (x-values), and the range represents all possible output values (y-values) of a function.