it would be very easy if graph is used...

the range of the funtion would be most of the times infinity.

and the minimum value is decided by the equation given.

ensure that all the functions have them defined .which plays an imp role in deciding the domain of the function...

f(x) = |x| is the modulus function.

or, f(x) = x , x > 0

               0 , x = 0

              -x . x < 0

Clearly now x can take any real value, so domain of function is all real values.

Now for any real x, f(x) is always positive so range of f(x) is [0,infinity).

It is quite clear from graph of modulus function also. ( See Below )