gas gauge works backwards

Has someone worked on the pump or related things recently? How did this start?

just had car in shop and they changed fuel pump

There is your problem. It sounds like they either used the wrong parts or installed them wrong.

how do I find out if they used wrong parts or installed wrong

By pulling the fuel tank and fuel pump back out and inspecting it. Some of these pump units come without the sender, which has to be swapped from the old tank unit to the new one. If they somehow wired it wrong or installed it upside down this would cause what you have

See the picture below of the tank unit

after installing a new fuel pump assembly gas gauge reads backwards.
gas gauge was working before installing fuel pump.

check to see if wires going to sender are hooked up correctly. the ones inside the tank unfortunately arrow points to tan wire which goes to gauge purple goes to PCM.

I have a 2007 Impala that does not give me a correct reading on the fuel guage. I can fill it up and 5 minutes later the low fuel lsign on the dash comes on. Any suggestions on what it might be? Is it the float or a sending unit that might be bad? HELP!!!!!!!!!!!

most likely caused by the fuel level sensor. is it still under warranty being its a 2007

my gas gauge goes all over the place no matter how much gas is in the tank

the fuel level sender is bad in the tank and needs to be replaced.

Engine Performance problem
2004 Chevy Impala 6 cyl Front Wheel Drive Automatic
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I recently had my 2004 Impala SS in for various GM service items. The car as 70,000 Km on it.

As my wife drives it she notice or thought she was getting better gas mileage as the fuel gauge wasn't moving. After about 400 KM it suddently moved near the empty position. This has continued during the last 3 fill-ups.

there may be a dead spot in the fuel level sending unit in the tank, would have that checked out first.