To estimate $\lim_{x \to 1^+} g(x)$ using the graph, let's examine the behavior of $g(x)$ as $x$ approaches $1$ from the right side (values slightly greater than 1).

1. Identify the right-hand limit: Look at the values of $g(x)$ as $x$ approaches $1$ from values slightly greater than $1$.

2. Determine the approximate $y$-value: Following the graph as $x \to 1^+$, we see that $g(x)$ approaches the value $2$.

Conclusion

Therefore, based on the graph, we can estimate: $\lim_{x \to 1^+} g(x) = 2.$

Would you like further details, or have any questions about this?

Here are 5 related questions for deeper understanding:

1. What is the difference between a right-hand limit and a left-hand limit?
2. How would the answer change if we were asked for $\lim_{x \to 1^-} g(x)$?
3. What if we needed $\lim_{x \to 1} g(x)$ instead of just the right-hand limit?
4. How can we determine continuity at $x = 1$ using limits?
5. Why is it important to consider limits from both sides when evaluating a general limit?

Tip: To find one-sided limits, always look for values slightly above or below the target $x$-value on the graph to see what $y$-value the function approaches.