To determine the domain and range of the piecewise function shown in the coordinate plane:

Domain:

The domain refers to all possible values of $x$ for which the function is defined. Looking at the graph, the function starts at $x = -5$ (open circle) and continues to $x = 3$ (closed circle).

Thus, the domain is: $-5 < x \leq 3$

Range:

The range refers to all possible values of $y$ that the function outputs. From the graph, the smallest value of $y$ is $y = -5$ (open circle) and the largest value is $y = 3$ (closed circle).

Thus, the range is: $-5 < y \leq 3$

Final answer:

• Domain: $-5 < x \leq 3$
• Range: $-5 < y \leq 3$

Do you want more details or have any questions?
Here are 5 related questions to explore further:

1. How would you write the piecewise function for this graph?
2. How do open and closed circles affect the domain and range of a function?
3. What is the significance of having a piecewise function compared to a continuous function?
4. How can you determine if a piecewise function is continuous at a certain point?
5. How can you graph a more complex piecewise function given its equation?

Tip: Always observe the endpoints carefully to determine whether they are included or excluded when calculating domain and range.