Determine the points at which the function f below has discontinuities. For each

Question

Determine the points at which the function f below has discontinuities. For each point state the conditions in the continuity checklist that are violated. In order for f to be continuous at a, the following three conditions must hold. f(a) is defined (a is in the domain of f). lim f(x) rightarrow a f(x) exists. lim f(x) rightarrow a f(x) = f(a) (the value off equals the limit of f at f(x) is discontinuous at x = 1,2,3 . Select the correct choice below and, if necessary, fill in the answer box within your choice. The point(s) at x = violate(s) the first condition in the continuity checklist. No points violate the first condition in the continuity checklist.

Explanation / Answer

the point at X=1 is not in the domain of function since the function does not attains any definite value at 1 i.e. f(1) is undefined.

Similarly, X=3 is not in the domain of the function. It is marked by a hollow circle.

therefore X=1,3 violates the first condition.

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