Let's analyze the graph of $f(x)$ from the image to answer the questions.

Part A: Identify all the x-values in the interval (-4, 5) where the graph of $f$ is not continuous.

A function is not continuous at a point if there is a break, jump, or hole in the graph at that point.

From the graph:

• At $x = -1$, there is a hole, indicating that $f$ is not continuous at this point.
• At $x = 1$, there is a jump discontinuity, so the graph is not continuous here as well.

Thus, the x-values where the graph is not continuous are: $x = -1, \quad x = 1$

Part B: Identify all the x-values in the interval (-4, 5) where the graph of $f$ is not differentiable.

A function is not differentiable at a point where:

1. The function is not continuous (since differentiability implies continuity).
2. The graph has a sharp corner or cusp.
3. There is a vertical tangent.

From the graph:

• At $x = -1$ and $x = 1$, since the graph is not continuous, it is also not differentiable.
• At $x = 0$, there is a sharp corner, so the function is not differentiable at this point as well.

Thus, the x-values where the graph is not differentiable are: $x = -1, \quad x = 0, \quad x = 1$

Would you like more details on this or any further clarifications?

Here are 5 related questions to deepen your understanding:

1. What is the formal definition of continuity at a point?
2. How does differentiability relate to continuity?
3. Can a function be continuous but not differentiable? Provide an example.
4. What are the different types of discontinuities a function can have?
5. What is the geometric meaning of a "sharp corner" in a graph?

Tip: A function is always differentiable where its graph is smooth and continuous, but keep an eye on points with sharp turns or jumps—those are places of non-differentiability!