From the description of the graph, it appears that the function $f$ has two distinct curves that exhibit features suggesting points where the function is not differentiable. Here’s a breakdown:

1. At $x = -2$: The curve makes a sharp turn upwards. Sharp turns or cusps in a graph indicate points where the derivative is undefined because the slope changes abruptly. Therefore, $f$ is not differentiable at $x = -2$.

2. At $x = 1$: There is a jump discontinuity between the two curves. The first curve stops at an open point, and the second curve starts from a closed point. A jump discontinuity is a common cause for non-differentiability because the function is not continuous at this point, which is a requirement for differentiability.

3. At $x = 3$: The second curve appears to make a sharp horizontal turn at $x = 3$. Just like at $x = -2$, this sharp turn indicates that the derivative does not exist because the slope abruptly changes.

Thus, the numbers at which $f$ is not differentiable are: $x = -2, 1, 3$

Would you like more details on how differentiability is determined?

Here are 5 related questions for further practice:

1. What is the relationship between continuity and differentiability?
2. How do you identify points of non-differentiability from a graph?
3. Can a function be continuous at a point but not differentiable?
4. What is the difference between a corner and a cusp in terms of differentiability?
5. How do you determine differentiability analytically for piecewise functions?

Tip: For a function to be differentiable at a point, it must be continuous there, and its left-hand and right-hand derivatives must be equal.