Final Answer:
The functions' continuity at x=1 depends on the limit of the function as x approaches 1.
Step-by-step explanation:
For a function to be continuous at a point, three conditions must hold: the function must be defined at that point, the limit of the function as x approaches that point must exist, and the limit must equal the function's value at that point.
To determine continuity at x=1, evaluate the function's limit as x approaches 1 from both the left and right sides. If these limits are equal and the function is defined at x=1, the function is continuous at that point. This involves calculating the function's limit as x approaches 1 and checking if it matches the function's value at x=1. If these conditions hold true, the function is continuous at x=1; otherwise, it is discontinuous.