Problem refer to the greatest integer function, which is denoted by x and is defined as x greatest integer curren x For example 3 6 greatest integer curren 3 6 4 2 greatest integer curren 2 2 2 5 greatest integer curren 2 5 2 The graph of f (x) x is shown There, we can see that x 2 for 2 curren x x...

A Since f is continuous from the right at x 2 B Since f is no ...

Problem refer to the greatest integer function, which is denoted by [x] and is defined as [x]

Question:

Problem refer to the greatest integer function, which is denoted by [x] and is defined as
[x] = greatest integer ‰¤ x
For example
[-3.6] = greatest integer ‰¤ -3.6 = -4
[2] = greatest integer ‰¤ 2 = 2
[2.5] greatest integer ‰¤ 2.5 = 2
The graph of f (x) = [x] is shown. There, we can see that
[x] = -2 for -2 ‰¤ x [x] = -1 for -1 ‰¤ x [x] = 0 for 0 ‰¤ x [x] = 1 for 1 ‰¤ x [x] = 2 for 2 ‰¤ x And so on.

(A) Is f continuous from the right at x = 2?
(B) Is f continuous from the left at x = 2?
(C) Is f continuous on the open interval (1,2)?
(D) Is f continuous on the closed interval [1,2]?
(E) Is f continuous on the half-closed interval [1,2)?