https://file.aiquickdraw.com/mathbot/file/17268534997892untlt5e.jpg

Let's analyze the graph and the given statements one by one.

### Statement I: 
\[
\lim_{{x \to 2^-}} g(x) = \lim_{{x \to 2^+}} g(x)
\]

From the graph, as \( x \to 2^- \) (approaching from the left) and \( x \to 2^+ \) (approaching from the right), both limits approach 1. Therefore, the left-hand and right-hand limits are equal:
\[
\lim_{{x \to 2}} g(x) = 1
\]
Thus, **Statement I is true**.

### Statement II:
\[
\lim_{{x \to 6}} g(x) \text{ does not exist}
\]

From the graph, as \( x \to 6^- \) (from the left), \( g(x) \to 2 \), and as \( x \to 6^+ \) (from the right), \( g(x) \to -2 \). Since the left-hand and right-hand limits are not equal, the limit does not exist. Therefore, **Statement II is true**.

### Statement III:
\[
\lim_{{x \to 2}} g(x) = g(2)
\]

From the graph, we see:
- \( g(2) = 3 \)
- \(\lim_{{x \to 2}} g(x) = 1\) (as calculated from Statement I).

Since the limit as \( x \to 2 \) is not equal to \( g(2) \), **Statement III is false**.

### Conclusion:
The true statements are **I and II**. Therefore, the correct answer is **(C) II and III only**.

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Would you like more details or further explanations? Here are some additional related questions:

1. What does it mean for a limit to exist at a point?
2. How can you visually determine if a function is continuous at a point?
3. What is the significance of a jump discontinuity?
4. How do left-hand and right-hand limits work in piecewise functions?
5. Can a function have a limit at a point where it is not defined?

**Tip:** Always check both the left-hand and right-hand limits at a given point to ensure whether the overall limit exists.

The graph shows the function g(x). Which of the following statements are true?
I. lim g(x) as x approaches 2 from the left equals lim g(x) as x approaches 2 from the right.
II. lim g(x) as x approaches 6 does not exist.
III. lim g(x) as x approaches 2 equals g(2).

Analyze the limits of the function g(x) as shown in the graph at x = 2 and x = 6. Understand how left-hand and right-hand limits determine the existence of limits and learn the significance of discontinuities at these points.

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