The image shows a graph of a function $f(x)$ with specific x-values for which the continuity must be evaluated. The questions below the graph are asking about the continuity of the function at various points. Here's how to approach these types of questions:

1. Find Discontinuities: Look for points on the graph where the function either jumps, has a gap, or a hole. These indicate discontinuities.

2. Types of Continuity: The options given are:

   • Continuous from the right: The function approaches the value from the right-hand side at that x-value.
   • Continuous from the left: The function approaches the value from the left-hand side at that x-value.
   • Neither: The function is not continuous from either side at the given x-value.

3. Graph Interpretation: By analyzing the graph, we can determine the nature of continuity at the specified points.

Let's Address Each Question Below the Graph:

1. Evaluate at x = -4: At $x = -4$, the graph shows that the function approaches a certain value from the right, but there is no graph to the left of $x = -4$, implying:

   • The function is continuous from the right at $x = -4$.

2. Evaluate at x = 0: At $x = 0$, the graph seems to have a hole, indicating a discontinuity. Since there's no defined value, it is:

   • Neither continuous from the right nor from the left at $x = 0$.

3. Evaluate at x = 2: At $x = 2$, the function has a hole and a jump to another point. This suggests discontinuity, so it is:

   • Neither continuous from the right nor from the left at $x = 2$.

4. Evaluate at x = 5: At $x = 5$, the graph shows that the function continues smoothly, so it is:

   • Continuous from both sides (continuous from the right or left).

5. Largest Value of the Function: The largest value of the function appears to be at $x = 2$ (if we consider the highest point), but it depends on whether that point is considered valid based on continuity. If the largest value at that point is not defined (due to the discontinuity), you would evaluate elsewhere on the graph.

Do you need any further details or clarifications?

Here are five related questions for further exploration:

1. How do you formally define continuity at a point mathematically?
2. What are the implications of jump discontinuities on the behavior of a function?
3. How can you determine if a function is continuous over an interval?
4. What is the difference between pointwise continuity and uniform continuity?
5. How can you use limits to evaluate the continuity of more complex functions?

Tip: Always consider both the graphical and algebraic forms of a function when determining continuity at a point to ensure accuracy.