Let's analyze the graph and answer the questions.

(a) Domain and Range of the function $f$:

• Domain: The domain of a function is the set of all possible $x$-values (horizontal axis) for which the function is defined. From the graph, the function starts around $x = -2$ and ends around $x = 3$. So, the domain is approximately: $[-2, 3]$

• Range: The range is the set of all possible $y$-values (vertical axis) that the function takes. From the graph, the lowest point is around $y = -1$ and the highest point is around $y = 2$. So, the range is approximately: $[-1, 2]$

(b) Intervals where $f$ is increasing and decreasing:

• Increasing: A function is increasing where the graph is going upwards as $x$ increases. From the graph, the function is increasing from $x = -2$ to $x = -1$, and again from $x = 1$ to $x = 2$. So the intervals where the function is increasing are: $(-2, -1) \cup (1, 2)$

• Decreasing: A function is decreasing where the graph is going downwards as $x$ increases. From the graph, the function is decreasing from $x = -1$ to $x = 1$, and again from $x = 2$ to $x = 3$. So the intervals where the function is decreasing are: $(-1, 1) \cup (2, 3)$

Final answers:

• Domain: $[-2, 3]$
• Range: $[-1, 2]$
• Increasing: $(-2, -1) \cup (1, 2)$
• Decreasing: $(-1, 1) \cup (2, 3)$

Would you like further details or clarifications on any part of this?

Here are 5 related questions to explore:

1. How do you determine the domain and range for more complex functions?
2. What are the conditions for a function to be considered increasing or decreasing?
3. How would vertical or horizontal shifts affect the domain and range of a function?
4. Can a function be increasing and decreasing on the same interval?
5. How can you identify local maxima and minima from a graph?

Tip: When identifying where a function increases or decreases, focus on the behavior of the graph (going up or down) as you move from left to right along the $x$-axis.