Limit And Continuity

To determine which of the given statements about the function are true, we need to consider the continuity at the specified points.

1. Right continuous at :
   The right-hand limit as is:
   
   However, . Since the limit from the right at is not equal to , is not right continuous at .
2. Left continuous at :
   The left-hand limit as is:
   
   Since , the left-hand limit does not equal . So, is not left continuous at .
3. Right continuous at :
   The right-hand limit as is:
   
   With , the right-hand limit does not match . Hence, is not right continuous at .
4. Continuous at :
   The left-hand limit as is:
   
   The right-hand limit as is:
   
   Since for , we have:
   . As the limits from the left and right equal , is continuous at .

Therefore, the correct statement is: is continuous at .