bandwidth between the signal and the channel
If I understand correctly you would like to pass a bandpass signal of 4Khz bandwidth in the frequency range 6 to 10 Khz, but you would like to transmit this directly over a channel which has good channel gain in 1 to 5Khz. Clearly, the signal when passed over a channel with this frequency response will suffer complete degradation. 

Hence, we cannot transmit this signal directly over this channel. You could first downcovert the signal by 5 Khz and then transmit.