To determine where the function $f(x)$ is continuous based on the graph, we can observe any jumps, breaks, or asymptotes.

Observations from the graph:

• The graph seems to have several points where the function is not continuous.
• There is a clear vertical asymptote at $x = 0$, which suggests the function is not defined or has infinite behavior there.
• Additionally, it appears there are discontinuities at other specific points, marked by hollow circles, indicating possible jump discontinuities.

Conclusion for Continuity:

The function $f(x)$ is continuous on all intervals where there are no breaks, jumps, or vertical asymptotes.

Based on the graph, $f(x)$ appears continuous on the following intervals (in interval notation):

• $(-\infty, -6]$
• $(-6, 0)$
• $(0, 1)$
• $(1, 3]$
• $[3, 5]$

The points where $f(x)$ is discontinuous:

• At $x = 0$ (vertical asymptote)
• Possibly at some discrete points such as $x = 1$ and $x = 3$ due to potential jumps (hollow circles).

Let me know if you'd like more details or clarification.

Here are 5 follow-up questions related to continuity and functions:

1. What are the different types of discontinuities that can occur in a function?
2. How do you determine the continuity of a piecewise function?
3. Can you explain the Intermediate Value Theorem in the context of continuity?
4. What does it mean for a function to have a removable discontinuity?
5. How is the concept of limits connected to the continuity of a function?

Tip: When analyzing the continuity of a function, pay close attention to both the domain (where the function is defined) and any potential asymptotes or jumps, as these usually indicate discontinuities.