Question

What is the range of the function f(x) = |x − 1| − 2?

Answer 1

You obtain the graph of function $f(x)=|x-1|-2$ translating the graph of function $g(x)=|x|$ 1 unit left and 2 units down.

The range of the graph $g(x)=|x|$ is $[0,\infty]$. When you make the needed translations you can see that the range of the function $f(x)$ is $[-2,\infty]$.

Answer: $[-2,\infty]$.