https://file.aiquickdraw.com/mathbot/file/1727020869817lok7rgqs.jpg

From the graph provided, we are asked to evaluate the limit:

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

### Steps to Analyze the Limit:
1. **Check behavior from the left**: As \(x\) approaches -4 from the left (\(x \to -4^-\)), the function is increasing and seems to approach a value near \(y = 4\).
   
2. **Check behavior from the right**: As \(x\) approaches -4 from the right (\(x \to -4^+\)), the function is decreasing and also seems to approach the same value, \(y = 4\).

Since the function approaches the same value of \(y = 4\) from both the left and right sides of \(x = -4\), the two-sided limit exists and is equal to 4.

### Conclusion:
\[
\lim_{{x \to -4}} f(x) = 4
\]

Would you like further details, or have any questions about this process?

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Here are 5 related questions you might find interesting:
1. How do you determine if a limit exists based on a graph?
2. What is the difference between one-sided and two-sided limits?
3. How can limits help in determining continuity at a point?
4. What happens if the function approaches different values from the left and right of a point?
5. How can limits be used in the definition of derivatives?

**Tip**: If a function has different left-hand and right-hand limits, the overall limit does not exist at that point!

Determine the limit of the function f(x) as x approaches -4 from the provided graph.

In this example, we explore how to evaluate the limit of a function at x = -4 using a graph. The function appears to approach the same value from both the left and right sides, allowing us to conclude the limit exists. This is a useful method for understanding continuity and behavior near specific points.

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