Question

At what value or values of x is the (piece-wise) function
F(x)= x+4 if x ≤ -1
x^2 if -1 < x < 1
2-x if x ≥ 1
discontinuous?

Answer 1

Evaluate the function at the "joints" of the pieces, namely x=-1 and x=1.
If they evaluate to the same value from the left and from the right, the function is continuous. If they don't, the point is discontinuous.