1. The problem statement, all variables and given/known data Find the Fourier transform F(w) of the function f(x) = [e-2x (x>0), 0 (x ≤ 0)]. Plot approximate curves using CAS by replacing infinite limit with finite limit. 2. Relevant equations F(w) = 1/√(2π)*∫ f(x)*e-iwxdx, with limits of integration (-∞,∞). 3. The attempt at a solution I solved the integral and found the Fourier transform of f(x) to be: F(w) = 1/√(2π) * (2+iw)/(4+w2). I am pretty confident in my solution (but feel free to correct me if I'm wrong!). Where I have an issue is this.. F(w) is complex, so how do I plot it? Do I only plot the real part? How do the real and complex parts of F(w) relate to f(x)? I may have this question because I am still having a hard time fundamentally understanding the relationship between F(w) and f(x), so any information on this topic would be welcome. Describing F(w) as a function that determines the coefficient (contribution) of eiwx in f(x) makes some sense, (as explained in the below link): http://math.stackexchange.com/questions/1002/fourier-transform-for-dummies (answer #2, with plot of sines). However I still am confused how a complex-valued F(w) is tied in. Thanks!