Let's go through the information and solve the problem based on the graph provided.

The problem asks you to find:

a. $g(0)$
b. $\lim_{x \to 0} g(x)$
c. $g(1)$
d. $\lim_{x \to -1} g(x)$

From the graph:

1. For $g(0)$:

   • Look at the value of $g(x)$ when $x = 0$. The graph shows a point at $(0, 2)$. So, $g(0) = 2$.

2. For $\lim_{x \to 0} g(x)$:

   • The limit as $x$ approaches 0 is the value the function tends towards from both sides. Since the graph is continuous at $x = 0$ and the value at that point is 2, we have: $\lim_{x \to 0} g(x) = 2$

3. For $g(1)$:

   • Check the graph at $x = 1$. It shows the point at $(1, 0)$, so $g(1) = 0$.

4. For $\lim_{x \to -1} g(x)$:

   • As $x \to -1$, the function approaches a value. The graph shows continuity around $x = -1$, and the value approaches 1. Hence: $\lim_{x \to -1} g(x) = 1$

Summary:

• a. $g(0) = 2$
• b. $\lim_{x \to 0} g(x) = 2$
• c. $g(1) = 0$
• d. $\lim_{x \to -1} g(x) = 1$

Would you like to dive into any of these steps for more details?

Here are 5 related questions you might find helpful:

1. What is the difference between a function value and a limit?
2. How do we evaluate limits from the left-hand and right-hand side of a point?
3. What happens when a function is not continuous at a point?
4. How do you interpret limits at infinity?
5. Can a function be undefined at a point but still have a limit?

Tip: Always check for continuity at the point when determining both the function's value and the limit.