Let's analyze the graph to answer the questions about the limits and function values. From the image:

1. $\lim\limits_{x \to -2} g(x)$:

   • As $x$ approaches -2 from both sides (left and right), it seems like the graph approaches a specific value. From observation, it appears that $g(x)$ approaches 0 as $x$ gets closer to -2.
   • Answer: $0$

2. $\lim\limits_{x \to -2^+} g(x)$:

   • The right-hand limit as $x$ approaches -2 appears to also approach 0, as the graph converges from both sides symmetrically.
   • Answer: $0$

3. $\lim\limits_{x \to 2^-} g(x)$:

   • As $x$ approaches 2 from the left side, the graph approaches a value of about 1.
   • Answer: $1$

4. $\lim\limits_{x \to 0} g(x)$:

   • As $x$ approaches 0 from both sides, the graph appears to converge to a value of approximately -2.
   • Answer: $-2$

5. $g(2)$:

   • The graph shows a hole at $x = 2$ and a filled dot at $y = 0$, meaning $g(2) = 0$.
   • Answer: $0$

If you'd like more details on limits or graphs, feel free to ask!

Related Questions:

1. What happens when a function has different left-hand and right-hand limits?
2. Can a function be discontinuous but still have a limit at a point?
3. How can you determine whether a function is continuous from its graph?
4. What is the difference between a point being undefined and a limit not existing?
5. How do limits relate to the concept of derivative?

Tip:

When analyzing limits graphically, always check the behavior of the function from both the left and right to determine if the two-sided limit exists.