https://file.aiquickdraw.com/mathbot/file/17270216864775qzk2u94.jpg

The problem asks for the limit:

\[
\lim_{x \to 2^-} f(x)
\]

where the function \( f \) is represented graphically. The limit is approaching \( x = 2 \) from the left side (denoted \( 2^- \)).

### Steps to analyze the graph:

1. **Left-hand limit at \( x = 2 \)**:  
   To find \( \lim_{x \to 2^-} f(x) \), we observe the behavior of the function as \( x \) approaches 2 from the left-hand side.

2. **Reading the graph**:  
   As we trace the graph from the left side towards \( x = 2 \), the function value increases up to 4. This is confirmed by the solid point at \( (2, 4) \), indicating that the left-hand limit is 4.

Thus, we conclude:

\[
\lim_{x \to 2^-} f(x) = 4
\]

Would you like further details on this solution, or do you have any questions?

Here are five follow-up questions related to limits and graph analysis:
1. What is the limit as \( x \) approaches \( 2^+ \) from the right-hand side of the graph?
2. What is the overall limit \( \lim_{x \to 2} f(x) \)?
3. How would you define continuity at a point using limits?
4. What is the importance of left-hand and right-hand limits in determining whether a function has a limit at a point?
5. How would the result change if the function were not defined at \( x = 2 \)?

**Tip**: When analyzing limits from a graph, always check the behavior from both sides and note whether the function is continuous at the point of interest.

Evaluate the limit \(\lim_{x \to 2^-} f(x)\) for the function \(f\) shown in the graph below. If the limit does not exist enter \(\emptyset\).

This problem involves evaluating the left-hand limit \(\lim_{x \to 2^-} f(x)\) from the given graph. The solution explores how to read the function values approaching x = 2 from the left-hand side, leading to the limit value of 4. Suitable for Grades 10-12 students learning about limits in calculus.

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