https://file.aiquickdraw.com/mathbot/file/1729603785224riqqgord.jpg

https://file.aiquickdraw.com/mathbot/file/1729603785224zpndrzax.jpg

To solve the problems regarding the limits of the function \( f(x) \) shown in the graphs, let's analyze the provided images. The first image represents the graph of the function, and the second image lists the specific limit questions:

### Analysis:
1. **\( \lim_{x \to -7} f(x) \)**:
   - As \( x \) approaches \(-7\), the graph indicates the value of \( f(x) \) converges towards approximately -3. Therefore, \( \lim_{x \to -7} f(x) = -3 \).

2. **\( \lim_{x \to 0} f(x) \)**:
   - Approaching \( x = 0 \) from both sides, the graph appears to converge to 0. Thus, \( \lim_{x \to 0} f(x) = 0 \).

3. **\( \lim_{x \to -3} f(x) \)**:
   - As \( x \) approaches -3 from both sides, the graph appears to approach approximately 3. So, \( \lim_{x \to -3} f(x) = 3 \).

4. **\( \lim_{x \to 6^-} f(x) \)**:
   - As \( x \) approaches 6 from the left, the value of \( f(x) \) seems to be around -2. Therefore, \( \lim_{x \to 6^-} f(x) = -2 \).

If you need further explanation on these limits or have other questions, feel free to ask.

### Related Questions:
1. How do you find a limit of a function from a graph?
2. What does it mean if a limit does not exist?
3. How can discontinuities affect the limit of a function?
4. How do you evaluate one-sided limits from a graph?
5. What are the different types of discontinuities in a graph?

### Tip:
When finding limits from a graph, always observe the behavior of the function as it approaches the point from both the left and right sides.

Find the limits of the function f(x) based on the given graph.

Analyze the graph of a function and find its limits as x approaches various values. This problem covers the concept of limits in calculus, exploring one-sided limits and their graphical interpretations. Suitable for students in Grades 10-12.

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