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To determine where the function \( g(x) \) is continuous based on the graph, we need to identify any breaks, jumps, or holes in the curve.

### Analysis of the graph:
1. **Discontinuities**:
   - There is an **open circle at \( x = -2 \)**, meaning the function is not defined at that point.
   - At **\( x = 0 \)**, there is a **jump discontinuity**; the graph jumps from one value to another without connecting.
   - At **\( x = 1 \)**, there is an open circle indicating another discontinuity.
   
2. **Continuity**:
   - The function appears continuous between:
     - \( (-\infty, -2) \) (since the graph is smooth before \( x = -2 \)),
     - \( (-2, 0) \) (continuous between \( x = -2 \) and \( x = 0 \)),
     - \( (0, 1) \),
     - \( (1, \infty) \).
   
### Intervals of continuity:
Based on this, the function \( g(x) \) is continuous on the following intervals:
- \( (-\infty, -2) \)
- \( (-2, 0) \)
- \( (0, 1) \)
- \( (1, \infty) \)

Would you like further details on continuity or have any other questions?

### Related questions:
1. What types of discontinuities are there, and how do they differ?
2. How can we use limits to check for continuity at a point?
3. What is the definition of a continuous function in terms of limits?
4. How does a jump discontinuity affect the differentiability of a function?
5. How would the graph of a piecewise function impact its continuity?

### Tip:
Always check for open and closed circles on a graph to determine points of discontinuity.

From the graph of g, state the intervals on which g is continuous.

Analyze the graph of a function g(x) to determine its intervals of continuity. This problem helps identify continuous and discontinuous regions, covering concepts like open circles, jump discontinuities, and smooth curves.

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