To solve the given problem, let us analyze the provided graph of $F(x)$ and focus on the behavior of $F(x)$ as $x \to 5^+$ (from the right-hand side of $x = 5$).

1. From the graph:

   • Locate $x = 5$ on the x-axis.
   • Observe the function's behavior as $x$ approaches $5$ from values slightly greater than $5$ (i.e., $x > 5$).

2. The y-value that the function approaches as $x \to 5^+$ determines the right-hand limit.

Now, let me calculate the answer based on the visual data in the graph.

Solution: From the graph, as $x \to 5^+$, the value of $F(x)$ approaches 6. Therefore:

$\lim_{x \to 5^+} F(x) = 6.$

Correct Choice: $\text{A. } \lim_{x \to 5^+} F(x) = 6.$

Would you like me to explain this further or clarify how limits from the right-hand side are evaluated?

Related Questions:

1. What is the difference between left-hand and right-hand limits?
2. How do you determine if a limit exists at a specific point $x = c$?
3. Can a function have a limit if there is a discontinuity at $x = c$?
4. How are one-sided limits useful in piecewise functions?
5. What are the conditions for a two-sided limit to exist?

Tip: Always check both the left-hand and right-hand limits when evaluating the existence of a limit at a point!