Let's analyze the graph and the limit problem you've presented:

The function in question is $g(x)$, and you're asked to evaluate $\lim_{{x \to 4.5}} g(x)$.

Step-by-step evaluation:

• We need to determine the limit of $g(x)$ as $x$ approaches 4.5.
• From the graph, as $x$ approaches 4.5 from both the left and the right, it is important to check if $g(x)$ approaches the same value from both sides.

1. From the left side: As $x \to 4.5^-$, the graph shows that the value of $g(x)$ approaches 1.
2. From the right side: As $x \to 4.5^+$, the graph also shows that the value of $g(x)$ approaches 1.

Since the function approaches the same value from both sides, the limit exists.

Thus, $\lim_{{x \to 4.5}} g(x) = 1$.

Answer:

The correct choice is: A. $\lim_{{x \to 4.5}} g(x) = 1$.

Let me know if you need more details or have questions.

Here are 5 relative questions to expand your understanding:

1. How is the concept of limits applied when a function has a jump discontinuity?
2. What is the difference between one-sided and two-sided limits?
3. What is the graphical interpretation of a limit?
4. When does a limit not exist for a given function?
5. How does continuity at a point relate to the existence of a limit?

Tip: When determining limits from a graph, always check the behavior of the function as it approaches the target point from both the left and right sides.