Let's analyze the graph you provided to answer the two parts (e) and (f):

(e) $\lim_{x \to 4} f(x)$:

This question asks for the limit of $f(x)$ as $x$ approaches 4. Looking at the graph near $x = 4$, the function appears to approach a value close to $3$. Therefore, we can estimate:

$\lim_{x \to 4} f(x) = 3.$

(f) $f(4)$:

This part asks for the value of the function at $x = 4$. From the graph, we can see that there is a small open circle at $x = 4$, which means that the function is not defined at this point.

Thus, we conclude: $f(4) \text{ is undefined.}$

Let me know if you want further details, or if you have any other questions!

Here are 5 related questions:

1. What is the difference between a limit and the function value at a point?
2. How do you determine whether a function is continuous at a point?
3. Can a function have a limit at a point where it is not defined?
4. What are removable and non-removable discontinuities in a graph?
5. How do we analyze the behavior of a function as $x$ approaches infinity?

Tip: When dealing with limits, always check for open or closed points at specific $x$-values, as these often indicate whether a function is defined or not at that point!