Write ` ` `f(x)=|x|` as a piecewise function. Find the domain and range of `f(x).`

Hello!

Actually, the function `|x|` (absolute value of `x` ) is defined as a piece-wise function:

`|x| = {(x if xgt=0),(-x if xlt0):}`

There are two "pieces" on which this function is defined using elementary functions, `(-oo, 0)` and `[0, +oo).`

The domain of a function is the set of numbers where it is defined. As we see, absolute value function is defined everywhere, so its domain is the entire set of real numbers `RR` (also we can write it as `(-oo, +oo)` ).

The range of a function is the set of all its values. Our function, `|x|,` is obviously always non-negative, so negative numbers are not in its range. Any non-negative number `y` is, in turn, in its range, because `|y| = y.` Thus the range of absolute value function is `[0, +oo).`