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The problem asks for the limit of the function \( f(x) \) as \( x \) approaches \(-1\), based on the graph provided.

Looking at the graph:

- For values of \( x \) approaching \(-1\) from the left (i.e., \( x \to -1^- \)), the graph approaches \( y = 6 \). 
- For values of \( x \) approaching \(-1\) from the right (i.e., \( x \to -1^+ \)), the graph also approaches \( y = 6 \).

Since both the left-hand limit and right-hand limit are equal and approach \( y = 6 \), we conclude that:

\[
\lim_{{x \to -1}} f(x) = 6
\]

Do you have any further questions, or would you like additional details on limits? Here are some related questions you might find useful:

1. What is the definition of a limit in calculus?
2. How do one-sided limits work, and how are they related to two-sided limits?
3. Can a function have a limit if there is a discontinuity at that point?
4. How can you visually identify the limit from a graph?
5. What are common mistakes when evaluating limits graphically?

**Tip:** Always check both the left-hand and right-hand limits when determining if the limit exists.

Determine the limit of the function shown in the graph as x approaches -1.

Learn how to determine the limit of a function as x approaches -1 based on a graph. This problem covers key concepts in calculus, including the limit theorem for one-sided limits, and how to visually identify limits from a graph. Suitable for students in Grades 10-12.

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