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The problem asks to determine the limit \(\lim_{x \to -3} f(x)\) using the given graph of the function \(f(x)\).

From the graph, we can observe the following as \(x\) approaches \(-3\):

- As \(x\) approaches \(-3\) from the left (\(x \to -3^-\)), the function \(f(x)\) seems to approach \(4\).
- As \(x\) approaches \(-3\) from the right (\(x \to -3^+\)), the function \(f(x)\) also seems to approach \(4\).

Since the left-hand limit and right-hand limit are equal, the two-sided limit exists, and we can conclude:
\[
\lim_{x \to -3} f(x) = 4.
\]

Would you like any further details or have any other questions?

Here are five related questions:
1. What is the definition of a limit in terms of left-hand and right-hand limits?
2. How do you determine if a limit does not exist (DNE)?
3. What is the difference between continuous and discontinuous functions in the context of limits?
4. Can a function have a limit at a point where it is not defined? Why or why not?
5. How can you use limits to analyze real-world phenomena, such as velocity or population growth?

**Tip:** Always check the behavior of a function from both sides of a point to determine the existence of a limit!

Use the graph of the given function f to determine the limit of f(x) as x approaches -3, if it exists. If the answer does not exist, enter DNE.

Determine the limit of f(x) as x approaches -3 using the graph of the function. Learn how to find left-hand and right-hand limits and conclude whether the limit exists.

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