First, where is that 3 foot jumper being added? Between the radio and that amplifier? If so, then the same impedance presented to that radio is now being presented to the amplifier. So, there should be no changes in SWR unless the output impedance of that amplifier is not the same as the radio's. The length of the feed line hasn't changed.
Second question, where are you measuring that SWR, between the radio and amplifier or between the amplifier and the antenna? If between the amplifier and the antenna, then see question one's results, the impedance of the amplifier's output is wrong (no change in feed line length).
There's a 'catch' in there. If the amplifier isn't 'ON' then there should be a by-pass length of feed line in there that goes around the amplifier from it's input connection to it's output connection. That short length of feed line is -short-, and unless there's a problem with it, shouldn't make -that- much difference in SWR. Just something else to check, is it 50 ohms as it should be? (I'm assuming all the coax is 50 ohms!)
If the feed line length makes any significant changes in SWR, and if all the feed line is 50 ohms, and if the output impedance and the input and output impedances of the amplifier are 50 ohms, then there's only one place left that can cause a significant change in SWR, the antenna isn't 50 ohms.
[I'm using the term 'significant' changes in SWR because nothing is absolutely perfect. A little bit of change is absolutely normal because none of the things being connected is going to be absolutely 'right'. They are all 'man-made'. If you are driving a 'service' truck, then you know that anyway, right?]
It can start to get complicated pretty quickly unless you know what's going on. That's why the long way of trying to explain this stuff. I hope some of it helps.
- 'Doc