To find the domain and range of the function $h$ from the graph provided, we will examine the x-values (domain) and y-values (range) that the function covers.

Domain:

The domain represents all the x-values for which the function is defined. From the graph, we see that:

1. There is a segment starting from $x = -5$ (open circle, not included) to $x = -3$ (closed circle, included).
2. There is another segment from $x = 0$ (closed circle, included) to $x = 2$ (closed circle, included).

So, the domain in interval notation is: $(-5, -3] \cup [0, 2]$

Range:

The range represents all the y-values that the function attains. From the graph, we observe:

1. The first segment has y-values ranging from $y = 3$ (open circle, not included) to $y = 5$ (closed circle, included).
2. The second segment has y-values ranging from $y = -3$ (closed circle, included) to $y = -1$ (closed circle, included).

So, the range in interval notation is: $(3, 5] \cup [-3, -1]$

Conclusion:

• Domain: $(-5, -3] \cup [0, 2]$
• Range: $(3, 5] \cup [-3, -1]$

Would you like more details, or do you have any specific questions?

Related Questions:

1. How do you determine the domain of a function from its graph?
2. What does an open circle versus a closed circle on a graph indicate?
3. How do you represent a union of intervals in interval notation?
4. What is the difference between domain and range?
5. Can you give an example of a function with a continuous domain but a discrete range?

Tip:

When finding the domain and range from a graph, always look at the x-axis for the domain and the y-axis for the range, paying attention to whether endpoints are included or excluded (open or closed circles).