From the graph you provided, we are asked to determine the domain and range of the function $g$. Let's analyze it step by step.

Domain:

The domain refers to all the possible values of $x$ for which the function is defined.

• The function $g$ starts at $x = -5$ (inclusive) and ends at $x = 5$ (inclusive). We observe that for all values of $x$ between $-5$ and $5$, the graph is continuous and well-defined.

Therefore, the domain of $g$ is: $\boxed{[-5, 5]}$

Range:

The range refers to all the possible values of $y$ that the function can take.

• The lowest point of the graph appears to be at $y = -3$, and the highest point appears to be at $y = 4$.
• As the graph spans continuously from $y = -3$ to $y = 4$, these values are included.

Thus, the range of $g$ is: $\boxed{[-3, 4]}$

Final Answer:

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

Let me know if you'd like more details on any part of this solution!

Follow-up Questions:

1. What is the significance of the domain and range in a real-world context?
2. Can you explain how the domain might change for different types of functions?
3. How would you find the domain and range algebraically without a graph?
4. What are some functions that have restricted domains, such as square roots or logarithms?
5. How do vertical asymptotes affect the domain of a function?

Tip:

When determining the domain and range from a graph, always focus on the horizontal span (domain) and the vertical span (range) of the curve.