From the graph provided, let's determine the domain and range of the function $g$.

Domain: The domain of a function refers to all the possible input values (x-values) for which the function is defined. Here, the function $g$ is defined for $x$ values starting just below $-5$ and ending at $3$. These points can be described as closed points since the graph includes the endpoints at $x = -5$ and $x = 3$. Thus, the domain in interval notation is: $\text{Domain: } [-5, 3]$

Range: The range of a function is the set of all output values (y-values) that the function can take. Observing the graph:

• At $x = -5$, $y \approx 2$
• The highest $y$-value appears at about $y = 4.5$ when $x$ is around $-4$.
• From $x = -4$ to $x = 3$, the function decreases, reaching a minimum of $y = -3$ at $x = 3$.

Therefore, the function reaches all $y$-values from about $-3$ to $4.5$. Thus, the range in interval notation is: $\text{Range: } [-3, 4.5]$

Here are the answers for the domain and range in the format requested:

• Domain: $[-5, 3]$
• Range: $[-3, 4.5]$

Would you like more details or help with another question?

Here are five related questions to expand upon the information:

1. How would the domain and range change if the graph extended beyond $x = 3$?
2. What happens to the domain and range if the graph is reflected over the x-axis?
3. Can you find a function that fits the graph provided?
4. How would you describe the behavior of the function between $x = -5$ and $x = -3$?
5. What mathematical concepts are applied when determining the domain and range from a graph?

Tip: When determining the range from a graph, look for the highest and lowest points the function reaches, along with any other constraints provided by the graph's context.