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The problem is asking to find \(\lim_{x \to 1^{-}} f(x)\) using the given graph. This represents the limit of \(f(x)\) as \(x\) approaches 1 from the left.

To solve this:

1. Locate \(x = 1\) on the graph (this is where the vertical line is closest to \(x = 1\)).
2. Focus on the behavior of the function as \(x\) approaches 1 from the left-hand side (\(x < 1\)).
3. As \(x\) gets closer to 1 from the left, the graph shows the function approaching a value of approximately \(y = -5\).

Thus, \(\lim_{x \to 1^{-}} f(x) = -5\).

Would you like further clarification or more details on this? Here are five related questions:

1. How is the limit defined for one-sided limits (from the left or right)?
2. What happens if the left and right limits differ at a point?
3. How do you calculate \(\lim_{x \to 1^{+}} f(x)\) using the same graph?
4. What is the overall limit \(\lim_{x \to 1} f(x)\), considering both sides?
5. How can limits be used to determine if a function is continuous at a point?

**Tip**: When dealing with one-sided limits, always check the graph's behavior specifically from the side indicated (left or right) for accuracy.

Find lim(x → 1⁻) f(x) using the given graph.

Learn how to determine the left-hand limit of a function as x approaches 1 using a graph. This calculus problem focuses on understanding limits, interpreting graphs, and applying the limit theorem.

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