To determine the domain and range of the function $h$ from the given graph:

Domain

The domain represents the set of all possible $x$-values for which the function is defined. Observing the graph:

• The left endpoint is at $x = -3$ (inclusive, as shown by a solid dot).
• The right endpoint is at $x = 5$ (inclusive, as shown by a solid dot).

Thus, the domain in interval notation is: $[-3, 5]$

Range

The range represents the set of all possible $y$-values that the function can attain.

• The highest point on the graph occurs at $y = 5$.
• The lowest point on the graph occurs at $y = -4$.

Therefore, the range in interval notation is: $[-4, 5]$

Final Answer

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

Would you like further details or have any questions?

Related Questions

1. How do you identify whether an endpoint is included or excluded in the interval?
2. What does it mean for a function to be continuous, and is $h$ continuous over its domain?
3. How can we find the domain and range of a function without a graph?
4. What is interval notation, and why is it useful in representing domains and ranges?
5. How can we express the domain and range if the graph had open circles instead of closed circles?

Tip

Remember that a closed dot on a graph indicates inclusion, meaning that the endpoint value is part of the domain or range. An open dot indicates exclusion.