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.