Using the FFT and plotting results

Hi,

I'm using the FFT to compute the FT of some data, and follow the example code used on the Mathworks FFT help page (shown below):

Fs = 1000;                    % Sampling frequency
T = 1/Fs;                     % Sample time
L = 1000;                     % Length of signal
t = (0:L-1)*T;                % Time vector
% Sum of a 50 Hz sinusoid and a 120 Hz sinusoid
x = 0.7*sin(2*pi*50*t) + sin(2*pi*120*t); 
y = x + 2*randn(size(t));     % Sinusoids plus noise
plot(Fs*t(1:50),y(1:50))
title('Signal Corrupted with Zero-Mean Random Noise')
xlabel('time (milliseconds)')
NFFT = 2^nextpow2(L); % Next power of 2 from length of y
Y = fft(y,NFFT)/L;
f = Fs/2*linspace(0,1,NFFT/2+1);
% Plot single-sided amplitude spectrum.
plot(f,2*abs(Y(1:NFFT/2+1))) 
title('Single-Sided Amplitude Spectrum of y(t)')
xlabel('Frequency (Hz)')
ylabel('|Y(f)|')

I just have a couple of queries:

1) where does the factor of 1/2 in the declaration of frequency come from? (f = Fs/2*linspace(0,1,NFFT/2+1);)/

2) when plotting why is the amplitude of the absolute value of Y(f) doubled? (plot(f,2*abs(Y(1:NFFT/2+1))))

Thanks in advance. Olie