To estimate $f(3)$ from the graph:

1. Locate $x = 3$ on the $x$-axis.
2. Identify the corresponding $y$-value of the function $f(x)$ at this point.

From the image, at $x = 3$, the graph seems to correspond to $y = -8$. Thus:

$f(3) \approx -8$

The correct choice is: $\boxed{f(3) = -8}$

Let me know if you need additional clarifications or calculations!

Follow-Up Questions:

1. What does the $y$-value of a function represent in real-world scenarios?
2. How can you determine the slope at a specific point on a graph?
3. What tools can you use to plot a similar function graph?
4. How would you estimate $f(x)$ for non-integer values like $x = 3.5$?
5. What happens to $f(x)$ as $x$ approaches larger positive or negative values?

Tip: Always check if the graph crosses grid lines accurately to avoid estimation errors!