The question asks to evaluate the right-hand limit of the function $f(x)$ as $x$ approaches $1$, which is written as:

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

Step-by-Step Solution:

1. Interpret the Graph: From the graph, examine the behavior of $f(x)$ as $x$ approaches $1$ from the right-hand side (i.e., $x > 1$).

   • As $x \to 1^+$, follow the graph of $f(x)$. The function value $f(x)$ approaches $1$.

2. Verify the Limit: The graph shows no discontinuity or oscillation near $x = 1$ from the right-hand side. The function smoothly approaches $1$ as $x \to 1^+$.

Final Answer:

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

The correct option is (B) 1.

Do you want further clarification or details? Here are 5 follow-up questions:

1. What is the difference between left-hand and right-hand limits?
2. How do we define continuity at a point using limits?
3. What happens if the left-hand limit and right-hand limit do not match?
4. Can a function have a limit at a point where it is undefined?
5. How do you determine whether a limit exists by examining a graph?

Tip: When evaluating limits from a graph, always trace the function's behavior closely from both sides of the point in question!