Conceptual question on FFT and chirp signal
Your question is deeper than you think. For signals whose spectra is time varying,like your chirp signal, you lose this spectral variation information in simple Fourier transforms. You must consult time-frequency analysis to retain the full information of both time variation and spectral variations.

Consider using "specgram()" function of matlab which computes and plots time-frequency spectograms of signals. 

Consider the following code from matlab:

  t=[0 0.5 1.0 1.5 2.0]; % time breakpoints
  f=[0 200 100 150 300];  % instantaneous frequency breakpoints
  p=polyfit(t,f,4);      % fit 4th order polynomial over time
  t=0:0.001:2;           % 2 secs @ 1kHz sample rate
  y=chirp(t,p);
  figure,specgram(y,128,1E3,128,120); % 2D time-frequency display


On the contrary a single FFT of the complete signal, which includes all the frequencies, nevertheless, loses their time variation information.