You obtain the graph of function [tex]f(x)=|x-1|-2[/tex] translating the graph of function [tex]g(x)=|x|[/tex] 1 unit left and 2 units down.
The range of the graph [tex]g(x)=|x|[/tex] is [tex][0,\infty][/tex]. When you make the needed translations you can see that the range of the function [tex]f(x)[/tex] is [tex][-2,\infty][/tex].
Answer: [tex][-2,\infty][/tex].
