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_x rightarrow a f(x) exists. lim_x rightarrow a f(x) = f(a) (the value of f equals the limit of f at a). f(x) is discontinuous at x =. Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The point(s) at x = violate(s) the first condition in the continuity checklist. B. No points violate the first condition in the continuity checklist. Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The point(s) at x = violate(s) the second condition in the continuity checklist. B. No points violate the second condition in the continuity checklist. Note that the third condition is automatically violated if either the first or the second condition is violated. Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The point(s) at x = violate(s) the third condition in the continuity checklist. B. No points violate the third condition in the continuity checklist.

Explanation / Answer

f(x) is discontinuous at x = 1,2,3

A> at x = 3 the function f(x) violates the first condition

A> At x = 2 the limit does not exist

that as while approaching x=2 form the left side the limit is = 2

and from the right the limit is =1

=> the second condition is violated at x = 2

A> at x = 2 condition 3 is violated

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