A function f is continuous at the point if the following conditions are satisfied.
1) is defined.
2) exists.
3) .

Determine the values of x, if any, at which the function is discontinuous. At each point of discontinuity, state the condition(s) for continuity that are violated.

A) ; conditions 1, 2
B) ; conditions 1, 2
C) ; condition 3
D) ; condition 2
E) Continuous everywhere

Question

A function f is continuous at the point  if the following conditions are satisfied. ​
1)  is defined.
2)  exists.
3)  .
​
Determine the values of x, if any, at which the function is discontinuous. At each point of discontinuity, state the condition(s) for continuity that are violated.
​  ​  ​ ​
A) ; conditions 1, 2 
B) ; conditions 1, 2 
C) ; condition 3 
D) ; condition 2 
E) Continuous everywhere

Quizplus · Accepted Answer

For the function to be continuous at a point, it must satisfy the three conditions mentioned. For option A, B and D, the function is not continuous because condition 2 is not satisfied at the given point. For option E, it is stated that the function is continuous everywhere, which means it is also continuous at the given point. Therefore, the only remaining option is C, where condition 3 is violated, which means the function is discontinuous at that point.

A Function F Is Continuous at the Point If