Question

How do you find the range of this?

Answer 1

you split the function into its three sections and calculated each one independently, afterwards you join the resulting sets

-x if x<-1:
(1,∞)

0 for -1≤ x ≤ 1:
{0}

x if x>1:
(1,∞)

range in total:
(1,∞) ∪ {0} ∪ (1,∞)=
(1,∞) ∪ {0}=
y∈R