Question

How do you find the domain and range of `f(x) = |x - 2|`?

Answer 1

Domain: `(-oo,+oo)`
Range: `[0, +oo)`

Explanation:

`f(x) = abs(x-2)`

`f(x)` is defined `forall x in RR`
Hence the domain of `f(x)` is `(-oo,+oo)`

`f(x)` may take all values `>=0`
Hence the range of `f(x)` is `[0,+oo)`

These can be seen from the graph of #f(x) below.
graph{abs(x-2) [-25.01, 26.32, -4.83, 20.84]}