Final answer:
To identify whether there's a removable or jump discontinuity at x = 3 and x = 5, the behavior of the function at these points must be examined. Removable discontinuities can be fixed by redefining the function.
Step-by-step explanation:
To determine the type of discontinuity at x = 3 and x = 5, we need to consider the behavior of the function at these points. A removable discontinuity occurs when a function is not defined at a certain point, yet the limit exists and is finite. In contrast, a jump discontinuity happens when there are two distinct finite limits from the left and the right side of a point.
Without the specific function provided, we cannot directly answer which type of discontinuity is present at x = 3 and x = 5. However, we can outline the general characteristics of each discontinuity type:
- A function with a removable discontinuity at a point can be made continuous by redefining its value at that point.
- If a function suddenly changes value as the input approaches a particular point from either side, it exhibits a jump discontinuity.
Gathering more information about the function in question, such as its definition or a graph, would allow us to categorize the discontinuity accurately.