The graph provided represents a function $g$ with a clear domain and range. Let's analyze the graph and determine both using interval notation.

Domain:

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

• The function starts at $x = -4$ and continues to $x = 3$.
• Therefore, the domain is from $-4$ to $3$.

In interval notation: $\text{Domain} = [-4, 3]$

Range:

The range of a function is the set of all possible output values (i.e., the $y$-values). From the graph:

• The function reaches a minimum $y$-value of $-5$ and a maximum of $5$.
• The maximum $y$-value at $5$ is not included, since there is an open circle at the point $(3, 5)$.

In interval notation: $\text{Range} = [-5, 5)$

Summary:

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

Would you like further details or have any questions?

Here are 5 related questions:

1. How do you interpret closed vs. open intervals on a graph?
2. Can the range of a function include an open interval at both ends?
3. How do asymptotes affect the domain and range of a function?
4. What is the difference between a continuous and a discrete function in terms of domain and range?
5. How do transformations (like shifts and stretches) affect the domain and range of a function?

Tip: When dealing with domain and range, always check for points where the function may be undefined or where there are open intervals to avoid including incorrect values.