Considered a function [tex] f(x) [/tex] with domain [tex] D [/tex], the range is the set of values reached by the function, i.e. the set
[tex] \{ y \in \mathbb{R} | \exists x \in D | y=f(x) \} [/tex]
We can see that the first portion of the graph ranges from a maximum of 2 to a minimum of -2, both included. So, the range of the first bit is [-2,2].
The second part of the graph ranges from a maximum of 6 to a minimum of 5, both excluded. So, the range of the first bit is (5,6).
Finally, the last part ranges from a minimum of 0 (excluded) to a maximum of what seems to be 1.5 (included). So, the range of the last bit is (0,1.5].
If we put together all these pieces, we have
[tex] [-2,2] \cup (5,6) \cup (0,1.5] = [-2,2] \cup (5,6) [/tex]
Since (0,1.5] is included in [-2,2] and adds nothing new. Written in inequality form the range is
[tex] -2 \leq y \leq 2 \lor 5 < y < 6 [/tex]
