The image shows a table where various limits and function values must be evaluated using the graph of $y = g(x)$. Let's go through each part step by step based on the graph:

A. $\lim_{x \to -3} g(x)$

• From the graph, as $x$ approaches $-3$ from both the left and right, the function values approach 1.
• Answer: 1

B. $\lim_{x \to -1} g(x)$

• As $x$ approaches $-1$ from both sides, the left limit approaches 4, but the right limit approaches -2.
• Since the left and right limits do not match, the limit does not exist.
• Answer: Does not exist

C. $\lim_{x \to -1^+} g(x)$

• As $x$ approaches $-1$ from the right, the function approaches -2.
• Answer: -2

D. $g(-1)$

• The value of $g(x)$ at $x = -1$ is marked by a filled circle at $( -1, -2 )$, meaning $g(-1) = -2$.
• Answer: -2

E. $\lim_{x \to -1^-} g(x)$

• As $x$ approaches $-1$ from the left, the function approaches 4.
• Answer: 4

F. $\lim_{x \to 4^+} g(x)$

• As $x$ approaches 4 from the right, the function approaches $-7$.
• Answer: -7

G. $\lim_{x \to 4^-} g(x)$

• As $x$ approaches 4 from the left, the function approaches $-2$.
• Answer: -2

H. $\lim_{x \to 7} g(x)$

• As $x$ approaches 7 from both sides, the function approaches $-7$.
• Answer: -7

J. $g(7)$

• The value of $g(x)$ at $x = 7$ is marked by a filled circle at $( 7, -7 )$, meaning $g(7) = -7$.
• Answer: -7

K. $\lim_{x \to 2^+} g(x)$

• As $x$ approaches 2 from the right, the function approaches $-2$.
• Answer: -2

Would you like any further clarification or details?

Here are five related questions for practice:

1. What is $\lim_{x \to 0} g(x)$ based on the graph?
2. How does the function behave as $x \to -5$?
3. What is $g(2)$ according to the graph?
4. Determine the left and right limits at $x = 5$.
5. What is the behavior of the graph as $x \to 8$?

Tip: Always compare the left-hand and right-hand limits to check if the overall limit exists at a given point.