The graph represents a function, and we are asked to determine the values of $x$ at which the function is not continuous.

Based on the visual inspection of the graph, here are the key observations:

1. There is a vertical asymptote near $x = -5$, which suggests that the function is not continuous at $x = -5$.
2. There is an open circle on the graph near $x = 4$, indicating a discontinuity at $x = 4$, as the function is not defined at this point.

Conclusion:

The function is not continuous at: $x = -5 \quad \text{and} \quad x = 4$

Would you like any further details or have any questions?

Related questions:

1. What are the types of discontinuities (e.g., jump, removable, infinite) at $x = -5$ and $x = 4$?
2. How can the concept of limits explain the discontinuity at $x = -5$?
3. Can you describe the difference between a removable discontinuity and an essential discontinuity?
4. How can you determine if a function is continuous using its derivative?
5. What does it mean for a function to be continuous on a closed interval?

Tip:

Discontinuities in a function can often be identified through vertical asymptotes or gaps in the graph, so it's important to check for these when analyzing continuity.