Question

Which of the following best describes the behavior of f(x)= (x+1)/absolute(x+1)
at x=-1
a. Jump discontinuity.
b. Removable discontinuity.
c. Infinite discontinuity.
d. The function is continuous.
e. All of these.
f. None of these.

Answer 1

|x+1|=x+1 when x+1>0 (x>-1)
|x+1|=-(x+1) when x+1<0 (x<-1)
so as x approaches f from the left, f approaches -1
and
as x approaches f from the right, f appraoches 1
this is a jump discontinuity

Answer 2

the graph looks something like:
----()
----|----
-1
()____

its a jump

Answer 3

thank you!!!

Answer 4

oh i understand thanx