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).