Shuts off when tank has less than qtr. of a tank and sputters when I "step on it on 2008 Chevrolet Tahoe

Rpm are not steady when stopped at a light.

replace the fuel filter. If this doesn't cure it, then the fuel pump is going out. With less than a 1/4 tank, the weight of the fuel isn't enough to keep the pump running at the proper pressure. Have the fuel system pressure checked.