To determine the intervals where the given function is continuous, I will analyze the graph. From what I can see, the function has the following key features:

1. Continuous segments: The function appears to be continuous at all points except one specific location.
2. Discontinuity at $x = -2$: The vertical dashed red line at $x = -2$ indicates a vertical asymptote or a discontinuity.
3. Open circle at $x = -6$ and $x = 4$: This suggests the function is not defined at these points, leading to discontinuities.

Therefore, the function is continuous in the following intervals:

• From $-\infty$ to $-6$
• From $-6$ to $-2$ (as there is a discontinuity at $x = -2$)
• From $-2$ to $4$
• From $4$ to $\infty$

Answer:

The function is continuous on the intervals: $(-\infty, -6) \cup (-6, -2) \cup (-2, 4) \cup (4, \infty)$

Would you like more details or have any further questions? Here are some related questions to explore:

1. What types of discontinuities can occur in a function's graph?
2. How do you determine if a function has a removable discontinuity?
3. Can a function be differentiable if it is not continuous?
4. What is the formal definition of a continuous function at a point?
5. How does the Intermediate Value Theorem relate to the continuity of a function?

Tip: When analyzing graphs for continuity, always look for vertical asymptotes, holes (open circles), and jumps in the graph as indicators of discontinuities.