- #1
peripatein
- 880
- 0
Hi,
For a function to be continuous, three conditions must be met - the function must be defined at a point x0, its limit must exist at that point, and the limit of the function as x approaches x0 must be equal to the value of the function at x0.
Now, assuming my function is f(x)=[x], which assigns an integer smaller than x to f(x). Thus, if 1≤x<2, f(x)=1.
The instructor claimed that this function is discontinuous for every integer x, which is perfectly clear just from looking at the graph of f(x), which is a step graph. He also mentioned that two of the three requirements for continuity are unmet in this case.
Which two requirements of the three above are unmet in this case?
For a function to be continuous, three conditions must be met - the function must be defined at a point x0, its limit must exist at that point, and the limit of the function as x approaches x0 must be equal to the value of the function at x0.
Now, assuming my function is f(x)=[x], which assigns an integer smaller than x to f(x). Thus, if 1≤x<2, f(x)=1.
The instructor claimed that this function is discontinuous for every integer x, which is perfectly clear just from looking at the graph of f(x), which is a step graph. He also mentioned that two of the three requirements for continuity are unmet in this case.
Which two requirements of the three above are unmet in this case?