Let's break down the information from the graph and solve the questions.

Domain and Range

1. Domain: The domain of a function is the set of all possible $x$-values that the function can take. From the graph, it appears that the function exists for $x$-values between $-6$ and $3$. Thus, the domain is: $\boxed{[-6, 3]}$

2. Range: The range of a function is the set of all possible $y$-values that the function can take. Looking at the graph, the function ranges from a minimum $y$-value of $0$ to a maximum $y$-value of $6$. Therefore, the range is: $\boxed{[0, 6]}$

Values of the Function

Next, we can use the graph to find specific function values.

• (a) $f(-3)$: At $x = -3$, the corresponding $y$-value on the graph is $6$. Therefore: $f(-3) = 6$

• (b) $f(0)$: At $x = 0$, the corresponding $y$-value is $4$. Therefore: $f(0) = 4$

• (c) $f(1)$: At $x = 1$, the corresponding $y$-value is $2$. Therefore: $f(1) = 2$

• (d) Values of $x$ such that $f(x) = 2$: The graph crosses $y = 2$ at two points: $x = 1$ and $x = -5$. Therefore, the values of $x$ for which $f(x) = 2$ are: $x = -5 \quad \text{and} \quad x = 1$

Would you like more details or further explanations on any of these parts? Here are some additional questions you might want to explore:

1. How do you find the domain and range of a function from a graph?
2. Can a function have a different domain and range for different intervals?
3. What are the properties of piecewise linear functions like this one?
4. How do you determine when a function is increasing or decreasing on a graph?
5. Can a function have more than one value of $x$ for a particular $y$?

Tip: Always verify the domain and range by carefully checking both the start and end points on the graph, including any breaks or discontinuities.