Find the x-values (if any)at which the function is not continuous.Which of the discontinuities are removable?
A) no points of discontinuity
B) (not removable), (removable)
C) (removable), (not removable)
D) no points of continuity
E) (not removable), (not removable)

Question

​Find the x-values (if any)at which the function  is not continuous.Which of the discontinuities are removable? ​
A) ​no points of discontinuity 
B) ​ (not removable), (removable) 
C) ​ (removable), (not removable) 
D) no points of continuity 
E) ​​ (not removable), (not removable)

Quizplus · Accepted Answer

The question does not provide the function, so we cannot determine the specific points of discontinuity. However, we know that a function can be discontinuous at a point if one of the following conditions is met:
1. The limit as x approaches the point from the left does not equal the limit as x approaches the point from the right.
2. The limit as x approaches the point does not exist.
3. The function is undefined at the point.
If a point of discontinuity is removable, it means that there is a hole or gap in the graph at that point. This can occur when a factor of the function cancels out or when the function is undefined at that point but can be "filled in" by assigning a value that makes the function continuous. 
Therefore, option C is the best choice, as it indicates that there are two points of discontinuity, one of which is removable.

​Find the X-Values (If Any)at Which the Function Is

Find the X-Values (If Any)at Which the Function Is