From the image you uploaded, it shows a question related to limits and continuity for a given function $g$ whose graph is provided. The question asks to evaluate or explain the limits for various values of $t$ based on the graph of $g(t)$.

Here’s the breakdown of the limits you need to evaluate based on the graph:

1. $\lim_{t \to 0^-} g(t)$

   • The limit as $t$ approaches 0 from the left-hand side.

2. $\lim_{t \to 0^+} g(t)$

   • The limit as $t$ approaches 0 from the right-hand side.

3. $\lim_{t \to 0} g(t)$

   • The overall limit as $t$ approaches 0 from both sides (this exists if and only if the left-hand and right-hand limits are equal).

4. $\lim_{t \to 2^-} g(t)$

   • The limit as $t$ approaches 2 from the left-hand side.

5. $\lim_{t \to 2^+} g(t)$

   • The limit as $t$ approaches 2 from the right-hand side.

6. $\lim_{t \to 2} g(t)$

   • The overall limit as $t$ approaches 2 from both sides.

7. $g(2)$

   • The actual value of the function $g(t)$ at $t = 2$, if defined.

8. $\lim_{t \to 4} g(t)$

   • The overall limit as $t$ approaches 4.

Steps to proceed:

• You’ll need to observe the behavior of the graph at each point $t = 0, 2, 4$ and check whether the left-hand and right-hand limits agree at those points.
• If the graph has a jump or discontinuity, the limit at that point might not exist.

Let me know if you want a detailed step-by-step evaluation of each of the limits, or if you have any specific question! Here's a list of relative questions:

1. How do you determine the limit from a graph at specific points?
2. What is the difference between left-hand and right-hand limits?
3. How do you evaluate if a limit exists or does not exist at a given point?
4. What happens if the left-hand and right-hand limits are not equal?
5. How do you interpret the value of the function at a specific point when evaluating limits?

Tip:

When analyzing limits from a graph, always pay attention to whether the graph has a hole, jump, or asymptote at the point of interest.