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The graph provided shows \( f(x) \), and we are tasked with determining where \( f(x) \) is continuous. A function is continuous if there are no breaks, jumps, or holes in the graph.

### Observations from the Graph:
1. There are visible discontinuities:
   - At \( x = -6 \): A jump discontinuity.
   - At \( x = 3 \): A hole (removable discontinuity).

2. The function appears continuous elsewhere.

### Continuity:
The function \( f(x) \) is continuous:
- On the intervals \( (-\infty, -6) \), \( (-6, 3) \), and \( (3, \infty) \).

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#### Related Questions:
1. What are the different types of discontinuities in a graph?
2. How do you test for continuity algebraically at a specific point?
3. Why is a jump discontinuity different from a removable discontinuity?
4. How can you modify \( f(x) \) to make it continuous everywhere?
5. What real-world problems rely on continuous functions?

**Tip:** Always examine both the left-hand and right-hand limits to confirm continuity at a point.

Based on the graph of f(x), determine where it is continuous.

Analyze the graph of f(x) to identify intervals of continuity and discontinuities. This lesson covers jump discontinuities, removable discontinuities, and how to classify them. Ideal for students in Grades 11-12 studying calculus or advanced algebra.

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