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The question asks for the left-hand limit as \( x \) approaches 7 from the left, or:

\[
\lim_{x \to 7^-} f(x)
\]

Looking at the graph provided, we can observe the behavior of the function \( f(x) \) as \( x \) approaches 7 from the left-hand side:

- As \( x \) approaches 7 from the left, the function \( f(x) \) is moving upward and seems to approach the value \( 1 \) just before \( x = 7 \). 
- The value of \( f(7) \) itself is not relevant since we only care about the value as \( x \) approaches 7 from the left (denoted by \( 7^- \)).

Thus, the left-hand limit is:

\[
\lim_{x \to 7^-} f(x) = 1
\]

The correct answer is \( \boxed{1} \).

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

Here are five questions that can further expand on the concept:
1. What is the right-hand limit of \( f(x) \) as \( x \to 7^+ \)?
2. How do you interpret the overall limit \( \lim_{x \to 7} f(x) \)?
3. What happens if the left-hand and right-hand limits are not equal?
4. How does a discontinuity affect the limit of a function?
5. Can a function have a limit at a point even if it's not defined at that point?

**Tip:** When calculating limits from the graph, focus on the behavior of the function near the point of interest, not the actual value at that point!

Find lim(x -> 7-) f(x) based on the provided graph of f(x).

Learn how to find the left-hand limit of f(x) as x approaches 7 using graphical analysis. This problem focuses on key calculus concepts such as one-sided limits and limit theorems. Suitable for students in Grades 11-12.

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