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The graph you provided shows two distinct linear segments, one starting at \( y = 16 \) and decreasing as \( x \to -\infty \), and another segment that also decreases as \( x \to \infty \). Since you are asking for the limit of \( f(x) \) as \( x \to -\infty \), we can focus on the left side of the graph.

### Observations:
- As \( x \to -\infty \), the function \( f(x) \) (the left-hand line segment) seems to approach a steep downward slope.
- The line passes through \( (0, -8) \) and continues downward, meaning the function values become more negative as \( x \to -\infty \).
  
From the appearance of the graph, it is clear that as \( x \to -\infty \), \( f(x) \) decreases without bound. Therefore:

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

This is because the left-hand line is decreasing indefinitely.

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Do you want more details or have any questions?

Here are 5 related questions for further understanding:
1. What is the slope of each linear segment in the graph?
2. How does the behavior of \( f(x) \) change as \( x \to +\infty \)?
3. What are the intercepts of the function on the x-axis and y-axis?
4. How can we express each line segment with a specific equation?
5. What are the potential domains and ranges of the function \( f(x) \)?

**Tip:** The limit as \( x \to -\infty \) indicates the long-term behavior of the function on the far left of the graph.

Explore the concept of limits with a focus on the behavior of a linear function as x approaches negative infinity. This analysis includes graphical representation and theoretical understanding suitable for advanced high school students in grades 11-12.

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