The image shows a graph of a function $f(x)$ with labeled points, including maxima, minima, and intercepts. To determine the domain of the function $f(x)$, we need to look at the extent of the graph along the x-axis.

Domain Analysis:

The domain of a function consists of all the x-values for which the function is defined. Observing the graph:

• The leftmost point on the graph is $(-28, -6)$, so the smallest x-value in the domain is $x = -28$.
• The rightmost point on the graph is $(24, 6)$, so the largest x-value in the domain is $x = 24$.

Since the graph appears to be continuous between these two points without any breaks, the domain of $f(x)$ includes all x-values from $-28$ to $24$.

Conclusion:

The domain of $f(x)$ is the interval:

$[-28, 24]$

This means $f(x)$ is defined for all x-values from $-28$ to $24$ inclusive.

Would you like further details or have additional questions?

Here are some related questions that might interest you:

1. What is the range of the function $f(x)$ based on the graph?
2. How does the continuity of a function affect its domain?
3. Can you describe a scenario where the domain of a function is restricted to specific values?
4. What are the differences between open and closed intervals in a function's domain?
5. How would the domain change if the graph had breaks or holes?

Tip: When determining the domain from a graph, always check for any gaps or vertical asymptotes that might restrict the x-values where the function is defined.