Question

Locate the points of discontinuity in the piecewise function shown below.

-(x + 1)2 + 2 ; - < x < -1
f(x) = -x + 2 ; -1 < x < 2
(x-1) ; 2 < x <




no points of discontinuity
x = -1 and 2
x = 2
x = -1

Answer 1

this is much easier than it may seem
replace x by the values where the domain changes and see if you get the same number on both sides

Answer 2

if you replace x by -1 in the first formula you get
\[-(-1+1)^2+2=2\]and in the second formula you get
\[-(-1)+2=3\] and since they are not equal, you have a discontinuity at \(x=-1\)

Answer 3

now replace x by 2 in the second and third formula and see if they agree