Question

What is the domain and range of `y=-abs(x-5)`?

Answer 1

There is no restriction on `x`, so the domain is `-oo < x<+oo`

Explanation:

Range:
The absolute bars mean that `|x-5|` cannot be negative, so the function with the extra minus outside the bars cannot be positive.
`- oo < y<=0`
Maximum value will be reached at `(5,0)`
graph{-|x-5| [-3.88, 16.12, -7.64, 2.36]}