Let's analyze the graph of the function $f(x)$ step by step and solve the questions:

1. Find the domain, using interval notation: The domain refers to all the possible $x$-values where the function is defined. From the graph, the function extends from $x = -4$ to $x = 4$, inclusive of these values. Thus, the domain is: $\text{Domain} = [-4, 4]$

2. Find the range, using interval notation: The range refers to all the possible $y$-values the function can take. From the graph, the function goes as low as $y = -4$ (at $x = -1$) and as high as $y = 9$ (at $x = -3.5$). Thus, the range is: $\text{Range} = [-4, 9]$

3. Determine $f(0)$: From the graph, when $x = 0$, the corresponding $y$-value is $-2$. Therefore: $f(0) = -2$

4. Determine $f(4)$: From the graph, when $x = 4$, the corresponding $y$-value is $2$. Therefore: $f(4) = 2$

5. Determine the value of $x$ where $f(x) = -4$: From the graph, the function equals $-4$ at $x = -1$. Therefore: $x = -1$

Summary of Answers:

1. Domain: $[-4, 4]$
2. Range: $[-4, 9]$
3. $f(0) = -2$
4. $f(4) = 2$
5. $x = -1$ where $f(x) = -4$

Would you like further details or clarifications?

Here are five related questions for further practice:

1. What is the value of $f(-4)$?
2. How many x-intercepts does the function have?
3. Determine the local maximum and minimum points.
4. Is the function even, odd, or neither?
5. Find all values of $x$ where $f(x) = 0$.

Tip: When interpreting a graph, always check how the curve behaves at the endpoints and key points, as these often determine domain, range, and critical points.