How to calculate the range of change of a Local oscillator
To get the range limits for the LO, you must either add the IF to the both ends of the receiving range or subtract the IF from the both ends of the receiving range. The construction of the receiver states, is it add or subtract, but definitely not the both.

Before the IF filter there are available (assumed to have an ideal mixer + sinewave LO) all frequencies that are in radio's input filter's passband and have a signal, but shifted. Two instances occur for each frequency - one shifted downwards and one shifted upwards. The up and down shifts are equal to freq(LO). If the downshifts result negative results, forget the minus signs.