From the image, we can see the graph of the function $f$ and need to determine its domain and range in interval notation.

Observations:

1. The domain of a function is the set of all possible $x$-values for which the function is defined. By looking at the graph:

   • The $x$-values range from $-2$ to $3$, inclusive.
   • This gives the domain as: $[-2, 3]$

2. The range of a function is the set of all possible $y$-values the function attains. From the graph:

   • The lowest $y$-value is $-2$, and the highest $y$-value is $4$.
   • Both endpoints are included since the graph touches those values.
   • This gives the range as: $[-2, 4]$

Final Answer:

• (a) Domain: $[-2, 3]$
• (b) Range: $[-2, 4]$

Let me know if you would like further clarification or details!

Questions for Deeper Understanding:

1. What is the difference between domain and range in a function?
2. How do we identify whether endpoints are included in the domain or range?
3. How would the domain and range change if the graph extended indefinitely in either direction?
4. Can you determine whether this function is continuous from the graph? Why or why not?
5. How would this problem change if the function had gaps or vertical asymptotes?

Tip:

Always carefully observe the graph's endpoints and behavior at the edges to accurately determine the domain and range.