Based on the graph provided, the function $h(x)$ has a specific domain and range that we can extract visually from the plotted points.

Domain:

The domain of a function is the set of all possible input values (x-values) for which the function is defined. From the graph:

• The leftmost point is at $x = -4$.
• The rightmost point is at $x = 4$.

Thus, the domain is: $\text{Domain of } h = [-4, 4]$

Range:

The range of a function is the set of all possible output values (y-values). Looking at the graph:

• The lowest y-value is $y = -5$.
• The highest y-value is $y = 3$.

Therefore, the range is: $\text{Range of } h = [-5, 3]$

Summary:

• Domain: $[-4, 4]$
• Range: $[-5, 3]$

Would you like further details or explanations on this?

Here are some related questions to extend your understanding:

1. How can we determine the domain of a function if the graph isn't provided?
2. What is the difference between the domain and range in a function?
3. How do you identify whether a function is continuous or discontinuous from a graph?
4. Can a function have gaps in its domain? What does that imply about the graph?
5. How can we describe the behavior of the function $h(x)$ at the endpoints of its domain?

Tip: Always check for open and closed intervals on a graph to determine if values at endpoints are included in the domain and range.