To determine $\lim_{{x \to 3^+}} f(x)$, which represents the right-hand limit of $f(x)$ as $x$ approaches 3, we need to observe the graph near $x = 3$ from the right side.

From the graph:

• As $x$ approaches 3 from values greater than 3 (i.e., from the right side), the function $f(x)$ appears to approach a value of approximately 5, based on the height of the point right after $x = 3$.

Thus:

$\lim_{{x \to 3^+}} f(x) = 5$

Let me know if you'd like further details or if you have more questions! Here are 5 related questions to explore:

1. How is the left-hand limit $\lim_{{x \to 3^-}} f(x)$ different from the right-hand limit $\lim_{{x \to 3^+}}$?
2. What is the overall limit $\lim_{{x \to 3}} f(x)$ based on this graph?
3. How do we determine if a function is continuous at a point like $x = 3$?
4. What can be said about the behavior of the function at points where the graph has jumps or vertical asymptotes?
5. How would you interpret the limit $\lim_{{x \to -2}} f(x)$ based on the graph?

Tip: To find a limit graphically, always check whether you're looking from the left, right, or both sides at the point in question!