Find all x-values where x is discontinuous. For each discontinuity state which of the three conditions is not fulfilled. Can anyone help me with this?

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1 Answer
Teddy
Jun 28, 2018

See below.

Explanation:

#f# is discontinuous at #x=-3# because #f(-3)# does not exist (infinite discontinuity).

#f# is discontinuous at #x=-2# because #lim_(x->-2)f(x)# does not exist (jump discontinuity). This is because #lim_(x->-2^-)f(x)=-1/5# and #lim_(x->-2^+)f(x)=3# so since #lim_(x->-2^-)f(x)!=lim_(x->-2^+)f(x)#, #lim_(x->-2)f(x)# does not exist.

#f# is discontinuous at #x=0# because #f(0)# does not exist (removable discontinuity).

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