Question

Which graph represents the function f(x)=|x-2|-1

Answer 1

Option C is the correct answer

Answer 2

we have

$f\left(x\right)=-\left|x-2\right|-1$

using a graphing tool

see the attached figure

The vertex is the point $(2,-1)$

The domain is the interval-----------> (-∞,∞)

Domain is all real numbers

The range is the interval---------> (-∞,-1]

Range  is all real numbers less than or equal to $-1$

The answer in the attached figure