The problem asks for the limit:

$\lim_{{x \to 4^+}} f(x)$

This means we are trying to find the limit of the function $f(x)$ as $x$ approaches 4 from the right side (positive side).

Looking at the graph:

1. The curve of $f(x)$ as $x$ approaches 4 from the right (values slightly greater than 4) follows an upward trajectory.
2. At $x = 4$, the graph is continuous, and the value of $f(x)$ appears to be approximately $1$.

Therefore, the right-hand limit as $x \to 4^+$ is:

$\lim_{{x \to 4^+}} f(x) = 1$

Would you like further clarification, or is there anything else you want to explore related to this topic?

Here are some related questions you might find useful:

1. How do we determine the left-hand limit as $x \to 4^-$ from this graph?
2. What is the significance of a function being continuous at a point in relation to limits?
3. How can we calculate limits if the graph is not provided?
4. Can limits exist even if a function is undefined at the point being approached?
5. How are limits related to the concept of derivatives in calculus?

Tip: To determine limits graphically, always check the behavior of the graph on both sides of the point you're approaching, paying attention to any discontinuities.