https://file.aiquickdraw.com/mathbot/file/1726662468560gmubgd2z.png

To determine where the function \( f(x) \) is not differentiable, let's examine the graph carefully.

### Points of Non-Differentiability:
1. **At \( x = -2 \)**: 
   - There is a vertical asymptote at \( x = -2 \), meaning the function approaches infinity. The function cannot be differentiable at vertical asymptotes.

2. **At \( x = 0 \)**:
   - There is a cusp or a sharp corner at \( x = 0 \). Differentiability requires smoothness, and sharp turns result in non-differentiability.

3. **At \( x = 2 \)**:
   - The function has a jump discontinuity at \( x = 2 \), indicated by the gap between the open and closed points on the graph. Discontinuities, especially jumps, mean the function is not continuous, hence not differentiable.

4. **At \( x = 3 \)**:
   - There is another sharp point at \( x = 3 \), indicated by the abrupt change in the slope. Similar to \( x = 0 \), sharp turns or cusps imply the function is not differentiable.

### Summary:
The function \( f(x) \) is not differentiable at the following points:
- \( x = -2 \) (Vertical asymptote)
- \( x = 0 \) (Cusp or corner)


Consider the function f whose graph is shown. List, with reasons, all x-values at which f is not differentiable.

Examine the graph of a function to determine points of non-differentiability at x = -2, 0, 2, and 3. Learn about vertical asymptotes, cusps, and discontinuities. Suitable for advanced high school students.

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