L-1 space of integrable functions

If f is in L1 and delta > 0, then the L1 norm of f(delta*x)-f(x) goes to zero as delta goes to 1. I have been studying my text for two hours and still really don't understand it. Any thoughts?

By the way, I have some ideas--

If I can show that f is a continuous function of compact support, then I will know that f is dense in L-1. That will guarantee that there exists a function g in L-1 such that the L1 norm of f minus g is less than any epsilon (epsilon greater than zero).

rogerpodger