The question is asking for the value of the limit $\lim_{x \to 2} g(x)$, which refers to the value that the function $g(x)$ approaches as $x$ gets closer to 2 from both sides (left and right).

Key points from the description of the graph:

• There's an open circle at $x = 2$ between $y = 1$ and $y = 2$.
• The curve approaches this open circle as $x$ approaches 2 from both the left and right sides.
• A closed circle is plotted at $x = 2$ near $y = -2.4$, but this is the actual value of the function at $x = 2$, not the limit.

The function’s value at $x = 2$ (which is $-2.4$) doesn't affect the limit, because the limit is determined by the values that the function approaches from both sides of $x = 2$.

Since the open circle (which represents the value the function approaches) is midway between $y = 1$ and $y = 2$, a reasonable estimate for $\lim_{x \to 2} g(x)$ is $1.5$.

Conclusion:

The correct answer is: $\boxed{1.5}$

Would you like more details on how limits work, or have any other questions?

Related Questions:

1. What is the difference between a limit and the function value?
2. How does an open circle on a graph affect the limit?
3. Why is the function value at $x = 2$ irrelevant for the limit in this case?
4. How can limits be estimated from a graph?
5. What are left-hand and right-hand limits?

Tip:

Always check whether the limit exists from both directions. If the values from the left and right are different, the limit does not exist.