Looking at the graph provided, we are asked to determine the domain and range of the function $f$, as intervals or unions of intervals. Let's break it down:

Domain:

The domain of a function is the set of all possible $x$-values for which the function is defined. From the graph, the function starts at $x = -4$ and continues until $x = 4$. The function is continuous throughout this interval.

Thus, the domain is: $[-4, 4]$

Range:

The range of a function is the set of all possible $y$-values that the function can take. From the graph, the lowest $y$-value is $-4$, and the highest $y$-value is $4$. The function takes on all $y$-values between these two points.

Thus, the range is: $[-4, 4]$

Final Answer:

• Domain: $[-4, 4]$
• Range: $[-4, 4]$

Would you like further clarification on these concepts, or have any questions about this problem?

Here are five related questions to deepen your understanding:

1. What happens to the domain and range if the function is shifted vertically or horizontally?
2. How would you define the domain and range if the graph had discontinuities?
3. Can a function have the same domain but a different range?
4. How can you tell from a graph if a function is one-to-one?
5. What is the importance of identifying the domain and range when solving real-world problems?

Tip: Always check for any holes, vertical asymptotes, or breaks in the graph, as these can affect the domain and range!