The graph provided shows a continuous curve that starts at a point and descends downwards. Let's find the domain and range based on this graph.

Domain:

The domain refers to all possible $x$-values (horizontal axis) that the function $h(x)$ can take.

• The graph starts at $x = -3$ and moves to the right until $x = 2$, with no gaps or breaks.
• Therefore, the domain is the interval from $-3$ to $2$.

In interval notation, the domain is: $[-3, 2]$

Range:

The range refers to all possible $y$-values (vertical axis) that the function $h(x)$ can take.

• The highest point on the graph is at $y = 3$, and the graph descends downwards, reaching the lowest point at $y = -2$.
• Therefore, the range is the interval from $-2$ to $3$.

In interval notation, the range is: $[-2, 3]$

Would you like more details or clarification?

Here are 5 related questions to expand on this:

1. How do you determine the domain of a function from its graph?
2. What is the difference between closed and open intervals in domain/range?
3. How would the domain or range change if the graph were extended beyond these points?
4. What would the domain and range look like if the graph were a parabola instead of a curve?
5. How does knowing the domain and range help in understanding the behavior of functions?

Tip: Always check for any gaps or vertical asymptotes in the graph, as they affect the domain!