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What is ModifyingBelow lim With x right arrow 4.5 g left parenthesis x right parenthesis​? Choose the correct answer below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
ModifyingBelow lim With x right arrow 4.5 g left parenthesis x right parenthesisequals
  
enter your response here
​(Type an integer or a​ decimal.)
B.
ModifyingBelow lim With x right arrow 4.5 g left parenthesis x right parenthesis does not exist

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.

For the function g(x) graphed here, find the following limits or explain why they do not exist:
a. lim g(x) as x -> 4
b. lim g(x) as x -> 4+
c. lim g(x) as x -> 6
d. lim g(x) as x -> 4.5

Evaluate the limits of the function g(x) from a graph at various points, including x approaching 4, 4.5, and 6. This problem focuses on understanding one-sided limits, continuity, and conditions when limits do not exist. Suitable for students in Grades 11-12.

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