Consider the question:

A function g(x) = 3 - l2x - 4l is defined for the domain 0 <= x <= 5.
Sketch the graph of g(x) and state the range of g corresponding to this domain.

Approach: The most direct way is to remove the modulus sign. Let's see how we do that.

By the definition of modulus, |2x - 4| = 2x - 4 when 2x - 4 >= 0, i.e. x >= 2.
So when x >= 2, g(x) = 3 - (2x - 4) = 7 - 2x.

By the definition of modulus, |2x - 4| = -(2x - 4) when x < 2.
So when x < 2, g(x) = 3 + (2x - 4) = 2x - 1.

To sketch the final graph of g(x), we do these:
1. Between 0<= x < 2, sketch g(x) = 2x - 1.

2. Between 2 <= x <= 5, sketch g(x) = 7 - 2x.

From the sketch (go draw!), we obtain the range of g as [-3, 3].
The value of g(x) = -3 lies on g(x) = 7 - 2x when x = 5.
The value of g(x) = 3 is the location where both graphs meet when x = 2.

Finally, we note that g is a piecewise function, since it is made up of several pieces depending on the set of values that x takes.