How to shift resistance range of Linear Potentiometers by X ohms in the Positive or Negative direction?
If you want to have your potentiometer going from 10k to 20k, simply hook a 10k after the potentiometer (e.g. where you get your changed Voltage).

Formula: Potentiometer range: From x to 10k+x: Add a resistor of x to the potentiometer. If you want to extend the range, then you have to use another approach.