Let's analyze the graph provided to determine the domain and range:

Domain

The graph shows the x-values where the function exists. It starts at $x = -7$ and continues rightward. There's a break in the function where no y-values exist from $x = 1$ to $x = 4$, and then the function continues from $x = 4$ onwards indefinitely. Thus, the domain in interval notation is: $\text{Domain} = [-7, 1) \cup (4, \infty)$

Range

The range can be observed from the y-values the function takes:

• From $x = -7$ to $x = 1$, the y-values decrease from just above $y = -1$ down to approximately $y = -1$.
• From $x = 4$ and beyond, the function's y-values start just below $y = 0.2$ and seem to level off towards $y = 0$ as $x$ approaches infinity.

Thus, the range, noting that the graph does not appear to reach exactly $y = 0.2$ but gets arbitrarily close, is: $\text{Range} = [-1, 0)$

Would you like more details on how these intervals are determined or have any other questions? Here are a few related topics you might find interesting:

1. What is interval notation and how is it used?
2. How can breaks in a graph affect the domain and range?
3. How to find limits of a function graphically?
4. What are common features to identify in a graph of a function?
5. How to handle piecewise functions when determining domain and range?

Tip: When determining the domain and range from a graph, always check for breaks, holes, or asymptotes as these can significantly affect the intervals.