Given the piecewise function # 1-x,x<-1#, #(x^2)-x,-1<=x<=6#, #x-7,x>6#, is it continuous at x=-1 and -6?

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Answer 1 · 2015-12-22T04:19:21

It is continuous at #x=-1# and #x=-6#, but not at #x=6#.

*As a disclaimer, I assumed the #-6# at the very end of the question was supposed to be a #6# and solved accordingly. *

To solve, you simply plug in the bordering #x#-value and see if the two are the same.

For #x=-1#:
#1-(-1)#
#1+1#
#2#

#(-1)^2-(-1)#
#1+1#
#2#

So, #f(x)# is continuous at #x=-1#

For #x=-6#, the function is continuous because it is not a border of the piecewise.

For #x=6#:
#(6)^2 - (6)#
#36-6#
#30#

#(6)-7#
#-1#
So, #f(x)# is not continuous at #x=6#