  Space-based gravitational wave detectors cannot keep rigid structures and
precise arm length equality, so the precise equality of detector arms which is
required in a ground-based interferometer to cancel the overwhelming laser
noise is impossible. The time-delay interferometry method is applied to unequal
arm lengths to cancel the laser frequency noise. We give analytical formulas of
the averaged response functions for tensor, vector, breathing and longitudinal
polarizations in different TDI combinations, and obtain their asymptotic
behaviors. At low frequencies, $f\ll f_*$, the averaged response functions of
all TDI combinations increase as $f^2$ for all six polarizations. The one
exception is the averaged response functions of $\zeta$ for all six
polarizations increase as $f^4$ in the equilateral-triangle case. At high
frequencies, $f\gg f_*$, the averaged response functions of all TDI
combinations for the tensor and breathing modes fall off as $1/f^2$, the
averaged response functions of all TDI combinations for the vector mode fall
off as $\ln(f)/f^2$ , and the averaged response functions of all TDI
combinations for the longitudinal mode fall as $1/f$. We also give LISA and
TianQin sensitivity curves in different TDI combinations for tensor, vector,
breathing and longitudinal polarizations.
