To determine the x-values where the function $f$ is not differentiable, we need to look for points on the graph where there are:

1. Sharp Corners or Cusps: The function has a sudden change in direction.
2. Vertical Tangents: The slope becomes infinitely steep.
3. Discontinuities: The function jumps or has a break.

Analyzing the provided graph, we can identify these characteristics:

1. At $x = -4$: There is a sharp corner or cusp.
2. At $x = -1$: There is a discontinuity (the function jumps).
3. At $x = 1$: There is a cusp where the graph changes direction sharply.
4. At $x = 2$: There is a discontinuity (the function jumps).

Hence, the x-values where $f$ is not differentiable are: $x = -4, -1, 1, 2$

Would you like a more detailed explanation of these points?

Here are five related questions for further exploration:

1. What is the definition of differentiability at a point?
2. How can you determine differentiability from the derivative of the function?
3. Why is a function not differentiable at a corner or cusp?
4. What are the implications of a function not being differentiable at a point?
5. How does continuity relate to differentiability?

Tip: When analyzing a graph for differentiability, always look for sharp changes, breaks, or vertical segments, as these indicate where the derivative does not exist.