The problem asks us to evaluate the right-hand limit of the function $f(x)$ as $x \to 1^+$ using the given graph. Here's how we can approach it:

1. Examine the graph near $x = 1$:

   • From the graph, as $x$ approaches 1 from the right ($x \to 1^+$), the function appears to approach the value of $-2$.
   • There is an open circle at $(1, -2)$, indicating that $f(1)$ is not defined or has a different value. However, the right-hand limit concerns what the function approaches, not the actual value at 1.

2. Conclusion:

   • The right-hand limit of $f(x)$ as $x \to 1^+$ is $-2$.

Thus, $\lim_{x \to 1^+} f(x) = -2$.

Would you like a detailed explanation of how limits work or have any other questions?

Here are 5 related questions to deepen your understanding:

1. What is the definition of a one-sided limit?
2. How do open and closed circles on a graph affect the limit of a function?
3. How would the left-hand limit $\lim_{x \to 1^-} f(x)$ be evaluated from this graph?
4. Can a function be continuous if a limit exists but the function value at that point is different or undefined?
5. What would change if the limit asked for $\lim_{x \to 1} f(x)$, rather than the right-hand limit?

Tip: Always check both left-hand and right-hand limits to determine if a function has a two-sided limit!