https://file.aiquickdraw.com/mathbot/file/1729637627006bkw0cic3.jpg

The graph provided shows a piecewise function with various sections of line segments, suggesting potential discontinuities.

### Step-by-step analysis:

1. **Left-side segment**:
   - For \( x < -2 \), the function appears continuous, following a straight line. There is no apparent discontinuity for \( x < -2 \).

2. **Point at \( x = -2 \)**:
   - The graph shows a change in direction at \( x = -2 \), but no jump or break. The left and right-hand limits as \( x \to -2 \) seem to coincide with the function value at that point. Thus, the function is continuous at \( x = -2 \).

3. **Point at \( x = 0 \)**:
   - There is a break at \( x = 0 \). On the left side of \( x = 0 \), the function follows a downward sloping line, while on the right side, the function shifts upward (horizontal line) starting at a different height. Since the left-hand and right-hand limits as \( x \to 0 \) do not match, the function is **discontinuous at \( x = 0 \)**.

4. **Point at \( x = 1 \)**:
   - At \( x = 1 \), the graph shows a solid dot at a specific height, but the function continues as a horizontal line beyond this point. There seems to be no jump or gap here, implying continuity at \( x = 1 \).

### Conclusion:
The function is discontinuous at \( x = 0 \).

Would you like more details on this discontinuity or any other questions? 

Here are some related questions you might find interesting:
1. What are the types of discontinuities, and which one is at \( x = 0 \)?
2. How can limits help determine continuity?
3. Could a function be continuous but not differentiable?
4. How would the graph change if the discontinuity at \( x = 0 \) were removed?
5. Can a piecewise function always be made continuous?

**Tip**: When analyzing graphs for continuity, always check the left-hand and right-hand limits, as well as the function's value at the point.

Find all points where the function is discontinuous. (Graph shows a piecewise function with a break at x = 0.)

This problem involves analyzing the continuity of a piecewise function, identifying points of discontinuity, and understanding the left-hand and right-hand limits. The graph suggests a discontinuity at x = 0, providing insight into function behavior.

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