To solve this problem, we need to find the domain and range of the function $g$, which is represented by the graph.

1. Domain:

The domain of a function consists of all possible $x$-values for which the function is defined.

Looking at the graph:

• The function is defined from $x = -1$ to $x = 2$ (left to right on the x-axis).
• The graph does not go beyond these values, and the function is continuous between these points.
• Therefore, the domain is $[-1, 2]$.

2. Range:

The range of a function consists of all possible $y$-values that the function outputs.

From the graph:

• The $y$-values range from $-3$ (the lowest point) to $1$ (the highest point).
• Hence, the range of the function is $[-3, 1]$.

Final Answer:

• Domain: $[-1, 2]$
• Range: $[-3, 1]$

Would you like more details on how to interpret the graph?

Here are 5 related questions to deepen your understanding:

1. How do you determine if a function is continuous or discontinuous based on its graph?
2. What would the domain and range look like if the function included open intervals (i.e., points that are not included)?
3. How does the domain and range change if we shift the graph vertically or horizontally?
4. What happens to the domain and range if the graph has asymptotes?
5. Can a function have the same range but a different domain?

Tip: Always pay attention to whether points on a graph are solid (included in the function) or open (excluded from the function) when determining the domain and range!