Question

How do you write the absolute value function that is equivalent to `f(x)= -x-2 if x<-2` and `x-2 if x ≥-2`?

Answer 1

You can't. It is not an absolute value function.

Explanation:

Here is the graph of the function `f(x)`

As we can see, this is neither a `V` nor an inverted `V`. So it is not an absolute value function.