(a) Show that if f(x) has a Fourier transform, so does f(x - α), and F{f(x - α)} = e^-iwαF{f(x)}.

(b) Using (a), obtain formula 1 in Table III, from formula 2.

(c) Show that if f̂(w) is the Fourier transform of f(x), then f̂(w - α) is the Fourier transform of e^iαxf(x).

(d) Using (c), obtain formula 7 in Table III from 1 and formula 8 from 2.

f(w) = F(f) f(x) (1 if -b < x