Part (a): Numbers at which f is discontinuous and explanation

- From the given graph, we can observe that f is discontinuous at x = -2 and x = 2.

Explanation:

1. Discontinuity at x = -2:
- At x = -2, we can see that the graph of f has a "jump" or a sudden change in its value.
- The function approaches a certain value from the left side of -2, but as soon as it reaches -2, the function jumps to a different value.
- This jump indicates a discontinuity at x = -2.

2. Discontinuity at x = 2:
- At x = 2, the graph of f has a "hole" or a missing point.
- The function approaches a certain value from both the left and right sides of 2, but there is a gap or hole at x = 2 where the function is undefined.
- This missing point indicates a discontinuity at x = 2.

Part (b): Determining the continuity from the right, left, or neither for each number

1. Continuity at x = -2:
- To determine if f is continuous from the right or left at x = -2, we need to check if the limit of f as x approaches -2 from the right side (x > -2) is equal to the value of f at -2, and if the limit of f as x approaches -2 from the left side (x < -2)="" is="" equal="" to="" the="" value="" of="" f="" at="" />
- Since there is a jump at x = -2, the limit of f as x approaches -2 from both sides will not be equal to the value of f at -2.
- Therefore, f is neither continuous from the right nor from the left at x = -2.

2. Continuity at x = 2:
- To determine if f is continuous from the right or left at x = 2, we need to check if the limit of f as x approaches 2 from the right side (x > 2) is equal to the value of f at 2, and if the limit of f as x approaches 2 from the left side (x < 2)="" is="" equal="" to="" the="" value="" of="" f="" at="" />
- Since there is a missing point or hole at x = 2, the limit of f as x approaches 2 from both sides will not be defined.
- Therefore, f is neither continuous from the right nor from the left at x = 2.

Conclusion:

- From the given graph, we can conclude that f is discontinuous at x = -2 and x = 2.
- Furthermore, f is neither continuous from the right nor from the left at both x = -2 and x = 2.